Download Answers to Puzzle #15

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Answers to Puzzle #15
Showing 1 to 50 of 631 answers:
Answer #7535:
From: 14
School: 111
The measure of angle CBE is .5x.
There's lotsa ways to explain it, but here's a simple one:
Draw in the bisector of angle ACB. Since this is an isosceles triangle by
definition, this particular bisector is also an altitude, which means it meets
side AB at a right angle. And lo and behold, line EB is also perpendicular to
AB, so the bisector (we'll call the point at which it meets AB "F") and EB are
parallel. We know by the alternate interior angle theorem that m<FCB=m<CBE,
and we know by the def. of bisect that m<FCB=.5x. So, by transitivity,
whatever I said is true.
Answer #7536:
From: 362
School: 297
The angle CBE equals x/2.
The first thing I did was find the angle ABC.
I know that there are 180 degrees in the sum of a triangle's angles.
Angle ACB = x, so I know that the angle ABC = (180 - x)/2
I know that angle ABE = 90 degrees, so angle CBE = 90 - (180 - x)/2
CBE = 180/2 -180/2 +x/2
CBE = x/2
That was so simple I decided I should see if I missed an easier way. I then
saw that if I had drawn another ray from line AD, parallel to ray BE,
bisecting the angle ACB. 1/2 of ACE would be x/2. Making angle CBE equal to
x/2, because they are complementary angles.
Answer #7539:
From: 3939
School: 1144
The angle CBE is x/2 degrees.
The line joining C and the mid-point M of A and B is parallel to the
line BE. Therefore the angles CBE and MCB are equal. Since CM clearly
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disects angle ACB, MCB is of x/2 degrees and consequently CBE also has
the same value.
Answer #7542:
From: 3647
School: 1583
The measure of the angle is x:2
Decision 1:
The angle CBE = 90 – mABC. In the triangle ABC AC = CB, so
angles CAB and ABC are equal. Angle CBA = (180 – x) : 2 = 90 –
x:2 . Angle CBE = 90 – (90 – x:2) = 90 – 90 + x:2 = x:2.
Decision 2:
Let CK be a bisector of the angle ACB. Triangle ACB is an
isosceles, so CK is a perpendicular to AB and CK is parallel to
BE. So, angles KCB and CBE are equal, angle KCB is a half of
angle ACB and angle CBE equals x:2 .
Answer #7544:
From: 1695
School: 11
The angle CBE has a measure of 1/2 x
Especially since my class has been working on line and angle
properties, I knew almost instantly what I should try. If BC was a
transversal between two parallel lines, a relationship could be found.
Because the triangle abc is isoceles, a perpendicular bisector on
segment AB and an angle bisector on angle C would be the same. I
will call the midpoint of AB Y. I will call this new line Z, and it
is parallel to line E because both are at a right angle to the same
line. To finish this part, segment BC is a transversal to parallel
lines Z and E.
A conjeture we discovered just last week was that when a pair of
parallel lines are cut by a transversal, the alternate interior
angles are congruent. Therefore, angle BCY and angle CBE, the
alternate interior angles, are congruent.
Before, I discovered that line Z is an angle bisector of angle ACB.
So, the angle BCY is 1/2 x. Because angle BCY is congruent to angle
CBE, angle CBE measures 1/2 x.
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Answer #7545:
From: 3941
School: 205
The measure of angle CBE is (x/2) degrees.
Since we are given that AC = BC, triangle ABC is an isosceles
triangle. The isosceles triangle theorem allows us to conclude that
the base angles (angle CAB and angle CBA) are congruent to each
other; that is, measure of angle CBA = measure of angle CAB. Since
the sum of the interior angles of a triangle is 180, the sum of angles
CBA and CAB must be 180-x. Since CBA and CAB are congruent, each
angle measures (180-x)/2.
Since EBD is a right angle (measures 90 degrees), then measure of EBA
is also a right angle. Angle addition tells us that CBA + EBC = EBA =
90 degrees. So, EBC = 90 - CBA, and CBA = (180-x)/2. So, EBC = 90 ((180-x)/2). Now, since 90=(180/2), we can rewrite this as
EBC = (180/2) - (180-x)/2
= (180 - 180 +x)/2
= x/2.
Answer #7546:
From: 3942
School: 1146
The angle CBE is 90 degrees minus the degree of angle ABC.
Because EBD is a right angle, ABE must also be a right angle. The
angles ABC and CBE added together equall angle ABE, so by subtracting
angle ABC (we don't know what it is) from 90 we get angle CBE.
Answer #7547:
From: 3943
School: 1147
Angle CBE = x/2
Triangel ACB is an isocelese with vertex angle x. Therefore the base
angles are congruent and are each equal to (180-x)/2.
Angle CBA and CBD are a linear pair therefore angle CBD is = to
180-(180-x)/2. and angle CBE is = to 180-(180-x)/2-90
which simplifys to: 90-(180-x)/2
90-(90-x/2)
90-90+x/2
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therefore angle CBE = x/2
Answer #7548:
From: 1609
School: 466
The measure of angle CBE is 1/2x.
The pic shows that each side of ray BE must equal 90 degrees total.
Triangle ACB is isosceles, therefore it has to angles equal which are
then x/2. 90-x/2=0 -> 90=x/2. The angle is x/2 or 1/2x
Answer #7549:
From: 1484
School: 21
The answer of the question is angle CBE=x/2 degrees
Since in triangle ABC, AC=BC by given,therefor, angle CAB=angle CBA by
if sides then angles. Angle C=x degrees by given, and the sum of the
angles of a triangle is 180 degrees, so angle CBA is (180-x)/2=90-x/2
degrees. Since angle EBD is a right angle by given, so that angle EBD
is 90 degrees. And angle EBA is supplymentery with angle EBD (assume
from diagram), so that angle EBA=180-angle EBD=90 degrees. So that
the measure of angle CBE= angle EBA-angle CBA=90-(90-x/2)=x/2 degrees.
Answer #7550:
From: 1608
School: 466
The measure of the angle CBE is x/2.
WE know that if we add up the angles A, B, and C. We will get 180
degree's. That is the same for all triangles. Angle C is x degrees.
Angle A and angle B are 180/2-x/2, which can also be stated as 90-x/2.
Angle ABE is 90 degrees. To get the angle of CBE we have to subtract
angle ABC from angle ABE, to get angle CBE. 90-(90-x/2) The angle
CBE is x/2.
Answer #7551:
From: 1319
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School: 186
The measure of angle CBEis 1/2X.
I got this answer by first printing out the picture and then dividing
the triangle ABC vertically. Than at the top of my angle CBE I made a
line to make a triangle out of that. The line made a 90 degree angle
with the line I used to split the first triangle. Since there was two
90 degree angles and The rectangle made by the two triangles was split
derectally diagnally I infered that the angle CBE was 1/2X because in
the rectangle I made the split of X was equal to the angle CBE.
Answer #7552:
From: 1275
School: 466
The measure of angle CBE is .5x.
To find out the measure of CBE, you need to find the measure of angle
ABC. The total number of degrees in a triangle is 180. IF the measure
of side AC=BC, then angles A and B must also be equal. With x as a
given angle, you need to subtract x from the total of 180. This
leaves you with .5(180-x), or 90 -.5x. If the angle ABE equals 90
(because angle EBD is 90), then to find the measure of angle CBE, you
need to subtract 90-.5x from 90. The leaves you with the equation of
90-90-.5x= y (angle CBE). The 90's will cancel out leaving .5x=y.
Which gives you the answer of angle CBE=.5x.
The AB=BC was a typo. It was supposed to be AC=BC, to make the
triangle an icosolis one. As you can see i change it on the top of my
answer. The .5 came from the process of finding the measure of angles
A and B. If x is known, and there are 180 degrees in a triangle, then
the sum of angles A and B would equal 180-x. To find the measure of
just one of the angles, you need to divide this equation by 2, giving
.5(180-x) as stated above. Sorry I did not state this clearer, but we
were running short on time, and we figured you would see that that is
the measure of angles A and B.
Answer #7553:
From: 890
891
School: 466
The measurement of angle CBE is 1/2x degrees.
From your information we know that angle ABE is 90 degrees. Angle
A and angle B are both 90-1/2x. The way we found was x+90-1/2x+90-1/
2x=180. The angles would be supplementary. We know that angles CBA
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and CBE are equal to 90 degrees. Then we took 90-1/2x+b=90 and we
factored this down to be b=1/2x. So the measurement of angles CBE is
1/2x.
Answer #7554:
From: 2949
School: 803
The measure of angle CBE is .5x.
To start off, I plugged in 30 for x. Since I know that the other
angles ABC and BAC are congruent, I did 180-30=150 then 150/2 = 75, I
knew that ABC=BAC=75. Then I knew that angles ABC and CBE are
complementary since EBD is 90 degrees. I did 90-70 and got 15 degrees
for angle CBE.
I did the same process with x=40 and I got the measure of angle CBE=
20. I noticed a pattern that half of 30 was 15 and half of 40 is 20,
so I got the equation, Angle CBE=.5x
Answer #7555:
From: 1340
School: 186
The measure angle CBE is 1/2x.
First i drew the situation out. The make it exact i made a
perpendicualr besiector of the line and then mesured with a ruler to
make the triangle have sides with the same legnth. I then looked at
the figure to find realtionships between the angles, so i measured
them all. Then i drew a perpendicular bisector from a point not on a
line and i used point C. This formed a triangle I then noticed that
this was the same right triangle formed by bisecting angle C and
dividing triangle CAB into two. This lead me to believe that the
masure of angle CBE is 1/2x.
Answer #7556:
From: 1608
School: 466
The measure of the angle CBE is x/2.
WE know that if we add up the angles A, B, and C. We will get 180
degree's. That is the same for all triangles. Angle C is x degrees.
Angle A and angle B are equal because they are on a staright line and
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have an equal length lines to the point wihich causes both angle to be
equal. This triangle is an equalateral triangle which means that
there are 2 equal sides and 2 equal angles A and B are the equal
angles. so each of them are
180/2-x/2, which can also be stated as
90-x/2. Angle ABE is 90 degrees. To get the angle of CBE we have to
subtract angle ABC from angle ABE, to get angle CBE. 90-(90-x/2) The
angle CBE is x/2.
Answer #7557:
From: 875
School: 466
We figured out that angle CBE equals x/2.
The isoceles triangle ABC equals a total of 180 degrees. We came up
with an equation 180-2/x then we took the 90 degree angle ABE and make
an equation 90-.5x. Then we used those two eguations and came up with
the answer.
Answer #7558:
From: 884
885
School: 466
<CBE = 1/2x (Angle CBE equals one-half of x)
To do this problem you must first understand the law of exterior
angles. The law of exterior angles states that the exterior angle of
one side is equal to the sum of the two angles opposite it. In this
situation it states the <C + <A = The exterior angle of B. To put
this into an equation we know that <C is equal to x, and we can find >
A by taking 180 (which is the sum of all the angles), subtract x from
it (which is <C), and divide it by two (for angles A and B).
Therefore <A = 90 - 1/2x. Now that we know <C and <A we know that to
find <CBE we must subtract the 90 degree angle that is given to us.
We now can come to the conclusion that our equation is x + (90 - 1/
2x) - 90 = CBE. If you work this out you will find that it ends up as
CBE = 1/2x.
Answer #7560:
From: 1610
School: 466
The measure of the angle CBE is x/2.
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We found this because the line ABD if it were an angle would be 180
degrees. Sence both lines AC and CB are equal that makes both of the
angles A and B are equal. So with 180 as the total you can split that
into two equal peices of 90-x/2. With that you subtract your 90 from
that side to try to get x by it's self and get x/2 which is your
answer.
Answer #7563:
From: 2935
School: 803
Angle CBE equals .5x.
First, I determined that the measures of angles CAB & CBA must be
congruent, because triangle CAB is a scalene triangle. Next, I
plugged in a value for x. The first value that I tried was x=30
degrees. For this value of x, the two other angles combined must
equal 150 degrees. Therefore, angles CAB & CBA, each equal 75
degrees. Angle CBA is complementary to angle CBE. If x=30, then
angle CBE equals 15 degrees.
Next, I repeated the same process with x=40 degrees, x=50 degrees,
and x=60 degrees. For these values of x, I concluded that the
measures of angle CBE are 20 degrees, 25 degrees and 30 degrees,
respectively.
With this information, I concluded that the measure of angle CBE
equals one-half of the measure of angle x.
I hope that you find my answer satisfactory, Ms. Fetter.
have a very nice week, and reply to me as soon as you can.
Please
Answer #7564:
From: 1291
1290
School: 466
angle CBE equeals 1/2x
To solve this problem we used the Law of Exterior angles. This law
states that the sum of the measure of two interior angles is equal to
the measure of the exterior angle opposite the angles. This is to say
that the measure of angle BCA plus the measure of angle CAB is equal
to the measure of angle CBD. We see that the measure of BCA is
represented by variable x, so we needed to find what the measure of
CAB is equal to. We did this by taking 180, which is the total measure
of all the angles in the triangle, and subtracting x, the measure of
one of the first angle, and dividing this by two,the reason we divided
by two is because line AC is equal to CB we know that that angle CAB
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is equal to CBA. We also subtracted 90 from this equation because
this will subtract angle EBD from exterior angle CBD to give us angle
CBE. So we added angle x plus the angle of CAB (90-1/2x) minus 90 to
equal CBE. This gives us the answer 1/2x for the measure of angle CBE
Answer #7568:
From: 3944
School: 754
CBE WILL BE X/2
I will take the height D from the top, and because the triangle is
isoskeles, the height will aslo be bisector of angle ACB(angle
ACB=x=x/2+x/2).But the height(CD) and BE are // because they are
vertical at the same line(AB).So angle CBE=BCD=x/2 as inside and
alternate from verticals BE and CD which are intersected by BC.
Answer #7569:
From: 3359
School: 24
The measure of angle CBE is half of the measure of angle ABC.
To find this answer you start with knowing that angle EBA is a right
angle including the given angle as x. To find the measure of angle
CBE you would divide angle ACB by half. So the measure of angle CBE
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is one half the measure of ACB or 1/2x
Answer #7570:
From: 3945
School: 38
Angle CBE is 1/2x
If you draw a line that is perpinduclar to the line ADthat passed
throught the point C. this will split the vertices x in half. then
the line CB is the transversal . By being alternate interior angles
1/2 X is the measurement of CBA
Answer #7571:
From: 479
School: 24
Angle CBE is equal to 90-x degrees.
I think it would be easier for me to solve this problem by using a
simple proof format. It's given that angle EBD is a right angle.
Therefore, it is equal to 90 degrees. Angle ACB and EBC are
complimentary. I know that they are complimentary because I
traced angle ACB on a piece of paper and measured the angle.
Then, I traced angle EBC on another piece of paper and there
angle measures complimented each other (added up to 90
degrees.) Therefore, when you subtract "x" from 90 degrees, then
you are left with the measure of angle CBE being the expression, 90-x.
Answer #7572:
From: 3949
3948
School: 364
The
formula is 90- [(180-x)/2] = measure of angle EBC.
The first step in this process was to realize that the addition of all three
angle in a triangle are equal to 180 degrees. Also in knowing the Isosceles
Triangle Base Angles Theorem, which states that in an isosceles triangles the
two base angles are of congruent measure. Which in this case tell us that the
measures of angles CAB and CBA are equal. To make the problem easier, we just
worked with the 90 degrees that encompass the triangle and the angle in
question. Our next step was to figure out the angle measure of angle CBA, so
as to find the measure of its adjacent angle CBE. Our first step in this was
to subtract x(the measure of angle BCA) from the total 180 degrees of the
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triangle. In doing this we found the measure of the two base angles together.
In dividing them by two we found the measure of each base angle alone. Both
CAB and CBA. Last we subtracted this quotion from the 90 degree angle formed
by points E,B,A, giving us the soultion and the equation 90- [(180-x)/2].
Answer #7574:
From: 3950
School: 33
Angle CBE is 30 degrees
We started out by knowing that Angle EBD is 90 degrees. In adition to
that, we knew that sides CB and side AC were equal in length. Angle
ACB was x. Now that we have this information, we can start on the
problem. Since Sides AC and CB were equal in length, we also know that
angles CAB and CBA(in my problem, they were labeled as Angle y) were
equal in angle measures.So the equation that came straight through my
mind was (2*y+x=180). I then solved for x in terms of y giving the
answer x=180-2y. The other equation that came to mind was that (z+y=
90)in this case z being angle CBE. I then solved for y in terms of z
giving me an answer stating y=90+z. So know my equation was (180-2*z+
x=180). From there I solve for x in terms of z giving 2*z=x. From this
I can state that 1/2*x+y=90. I then came up with multiple answers.When
x was 80, y was 50 and z was 40. When I used x as 60, my answer came
for y came out to be 60 and my answer for z(Angle CBE) was 30.
Answer #7576:
From: 1690
School: 226
The measure of angle CBE is 1/2x degrees.
Since AC = BC, I knew that triangle ACB was an isosceles triangle and
therefore angle CAB = CBA because base angles of an isosceles
triangle are always equal. Because the measures of the angles in the
triangle must equal 180 degrees and angle ACB is already x, the sum
of angles CAB and CBA must equal 180 - x, so they each are
(180 - x)/2, or 90 - 1/2x. Because the measure of a straight line is
180 degrees and angle EBD is 90 degrees, the sum of angles EBC and
CBA must equal 90 since 180 - 90 = 90. Because the measure of angle
CBA is 90 - 1/2x, angle EBC is 90 - (90 - 1/2x) which equals 1/2x
degrees.
Answer #7579:
From: 2669
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School: 24
I found that angle CBE would be thirty degrees. This is because
triangle CBE is a thirty sixty ninety trianlge.
If you say that angle b + angle CBE = 90 degrees, then you need to
find angle b. By measuring the angles of triangle ACB you can find
that it is an equialangular triangle. Therefore Angle B = 60 and Angle
CBE = 30 degrees.
Answer #7581:
From: 4513
School: 38
the soultion and the equation 90- [(180-x)/2].
The first step in this process was to realize that the addition of
all three
angle in a triangle are equal to 180 degrees. Also in knowing the
Isosceles
Triangle Base Angles Theorem, which states that in an isosceles
triangles the
two base angles are of congruent measure. Which in this case tell us
that the
measures of angles CAB and CBA are equal. To make the problem
easier, we just
worked with the 90 degrees that encompass the triangle and the angle
in
question. Our next step was to figure out the angle measure of angle
CBA, so
as to find the measure of its adjacent angle CBE. Our first step in
this was
to subtract x(the measure of angle BCA) from the total 180 degrees of
the
triangle. In doing this we found the measure of the two base angles
together.
In dividing them by two we found the measure of each base angle
alone. Both
CAB and CBA. Last we subtracted this quotion from the 90 degree
angle formed
by points E,B,A, giving us the soultion and the equation 90- [(180x)/2].
Answer #7582:
From: 3954
School: 1152
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The measure of angle CBE is 90-(180-x)/2.
To solve this problem, first you have to realize that triangle ABC is an
isoceles triangle. An isoceles triangle has two sides of equal length. It
also has two angles of equal measure. I knew that angle A and angle ABC were
then congruent. The sum of the inside angles of a triangle is 180 degrees, so
x plus the sums of the other angles must equal 180. The two unmarked tri
angles will be the same, so I subtracted x from 180, then divided the answer
by two to get the measure of one of the angles.
Since angle EBD is a right angle, so is angle EBA. The measure of one of the
base angles of triangle ABC plus angle CBE will add up to 90 degreees also.
So I subracted that from 90 degrees.
Answer #7586:
From: 710
School: 449
Angle CBE is x/2 degrees.
Since AC=BC, therefore it implies that triangle ABC is isosceles.
The base angles of and isosceles triangle are congruent. Since the
sum of the angles of any triangle is 180 degrees, the base angles
therefore add up to 180-x. Each angle would then be (180-x)/2. Let
y=angle CBE. Since a straight angle is 180 degrees, therefore (180x)/2+y+90=180. Solve for y and you get x/2 degrees. Therefore angle
ACB measures x/2 degrees.
Answer #7589:
From: 2089
School: 22
The measure of the angle CBE will be 1/2x
First I wanted to find out the measure of angle ABC in terms of X.
The sum of the measures of a triangle is 180°.
So angle ABC + angle BCA + angle CAB = 180°
In triangle ABC, CA=CB, so angle ABC = angle CAB.(If two sides of a
triangle are equal, the angles opposite them are equal.) The measure
of angle BCA is given as x.
So angle ABC + angle ABC + x = 180.
2(angle ABC) + x = 180
2(angle ABC) = 180 - x
angle ABC = 180 - x
------2
Then I subtract the measure of angle ABC form 90°.(angle ABC is a
right angle, and the measure of a right angle is 90°.)
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the measure of angle CBE = 90 - (180 - x)/2
angle CBE = 90 - (90 - x/2)
the 90s cancel out and -x/2 becomes x/2
angle CBE = x/2
Answer #7590:
From: 18
School: 116
The Angle CBE is Half the Angle X
We have that AC = BC.
We know that Angles opposite to Equal Sides are Equal.
Then, Angle CAB = Angle CBA
Let the Measure of these Angles be Y.
Then In Triangle ABC,
By Angle Sum Property of Triangles,
X + Y + Y = 180 {Sum of Three Anlges of Triangle is 180}
X + 2Y = 180
2Y = 180 - X
Y = (180 - X) / 2 ------------> Equation 1
Since Angle EBD = 90
Angle ABE = 90 Degrees {By linear pair Axiom}
By the figure We know that
Angle ABE = Angle CBE + Y
That means,
Angle CBE + Y = 90
Y = 90 - Angle CBE.-------> Equation 2
From Equation 1 and 2,
(180 - X) / 2 = 90 - Angle CBE
90 - X / 2 = 90 - Angle CBE
Adding both side 90, We get
Angle CBE = 1 / 2 of Angle X
Angle CBE = 1 / 2 of Angle ACB.
Answer #7592:
From: 628
School: 226
angle CBE is two times angle ACB
First I started with the obvious facts given to me. Number one, angle
ABD is a straight angle measuring 180 degrees as is obvious in the picture.
Secondly, as given angle EBD is a right angle measuring 90 degrees.
Therefore, by the subtraction property of equality, 180-90=90 so angle ABE
equals 90 as well.
Now if you look at the picture you can see that angle ABE is made up of
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angle
ABC and angle CBE.
12/2/08 5:46 PM
The way I started was this:
If AC=BC then triangle ABC is isosceles. Therefore, angles CAB and CBA
are
congruent. Every triangle has a total of 180 degrees, one of which is x in
this case. So 180-x= the combination of angles CAB and CBA. I labelled them
both y since they are the same measure. So, 180-x = (y + y) or 2y.
Then I made another equation which was 90-y = z (z was my name for angle
CBE)
This originated from the initial information I was given. Next I combined the
two equations
180-x = 2y
90-y = z
and solved them for z...
y = (180-x)/2
90- [(180-x)/2] = z
180-180+x = 2z
x = 2z
z = x/2
Since z stood for angle CBE and x for angle ACB, when written out angle
CBE
is angle ABC divided in half so half of angle ABC.
Answer #7593:
From: 3956
School: 1155
angle CBE=x/2
<CAB=<CBA because triangle ACB is iscoceles.
m<CAB+m<CBA+m<ACB=180 sum of angles in a triangle equals 180.
m<CBA+m<CBA+x=180
substituation
2m<CBA=180-x
simplifying & subtraction prop. of equality
:m<CBA=(180-x)/2
Division property of =
:m<CBA=90-x/2
<ABE & <EBD form a Linear pair; Def. of a L.P.
<ABE is a right angle; If one of the angles of a L.P. is a right <,
then the other < is a right <,too.
:m<ABE=90
Def. of a right <
m<CBA+m<CBE=m<ABE
Angle addition postulate
90-x/2+m<CBE=90
substitution
m<CBE=x/2
simplification & subtraction property of =
---------
Answer #7595:
From: 3958
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12/2/08 5:46 PM
School: 229
The measure of angle CBE equals half of x.
To find the measure of angle CBE I found where the perpendicular
bisector of angle ACB was and drew it. Then seeing that ray BE was
parallel to the perpendicular bisector I conluded that angle CBE was
excalty half of angle ACB.
Answer #7598:
From: 1535
School: 14
The measure of angle CBE = x/2 degrees
1.
Mark diagram with what is given:
a. AC = BC (AB is congruent to BC)
b. Angle EBD is a right angle, which equals 90 degrees
c. Angle ACB equals x degrees
2.
We know that if 2 sides of a triangle are congruent, then the
angles opposite those sides are congruent. Therefore, angle
CAB is congruent to angle CBA.
3.
We know that the sum of the interior angles of a triangle is
180 degrees.
If angle ACB = x degrees, then the sum of the angles CAB and
CBA equals 180 - x. Because these 2 angles are congruent,
each angle (CAB and CBA) can be written as (180 - x)/2.
4.
Assign angle CBE as y.
5.
Angle EBD is a right angle and therefore equals 90 degrees
6.
Line ABD is a straight line and we know that a straight line
measures 180 degrees.
7.
Add the 3 angles: CBA {(180-x)/2} + CBE (assigned as y) +
EBD (90 degrees) and set them equal to 180 degrees.
(180-x)/2 + y + 90 = 180
8.
Solve for y (angle CBE) in terms of x.
9.
Multiply each of the terms of the equation by 2 to eliminate the
2 under the division sign in the first term.
Result:
10.
180 - x + 2y + 180 = 360
Simplify the equation and solve for y (angle CBE).
360 - x + 2y = 360
- x + 2y = 0
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12/2/08 5:46 PM
2y = x
y = x/2
11.
y (also called angle CBE) = x/2.
Answer #7601:
From: 2688
School: 24
The measure of angle CBE is x./2.
First of all I drew an altitude from angle ACB to segment AB, let's
label the intersecting point X. By the definition of altitudes, this
line is perpendicular to AB.
Since it is given that line AD and ray
BE are perpendicular, I was able to conclude that the altitude drawn
was parallel to ray BE from the theorem that states if two lines are
perpendicular to the same line then they are parallel to each other.
Also, this altitude is an angle bisector (dividing the angle into two
congruent parts), this is true because it is an isosceles triangle (at
least two congruent sides) and the center line XC is congruent to
itself (reflexive property), allowing the use of the hypotenuse-leg
congruence theorem I was able to prove that these are congruent
triangles. Corresponding Parts of Congruent Triangles Theorem gives
me the ability to conclude that these two angles are congruent
therefore, I was able to find that the measure of angle XCB is 1/2x
or x/2. Next, transversal CB cuts the parallel segments XC and BE and
allows me to use the theorem of alternate interior angles. This
states that if there is two parallel lines cut by a transversal, than
the alternate interior angles are congruent, thus stating that angle
XCB and CBE are both x/2.
Answer #7602:
From: 698
School: 448
Angle CBE equals x/2 degrees, where x can be any positive number.
We know that angle C equals x degrees. We also know that sides AC and BC are
congruent. This means that their opposite angles, angles A and B are also
congruent. Therefore, triangle ABC is isoceles, meanign that it has at least
two congruent angles and at least two congruent sides. There are 180 degrees
in a triangle. The measure of angles A and B would be 180 minus x divided by
2. That is because A and B are congruent, so you just need to divide the
difference between 180 (total degrees in a triangle)-x(one angle) divided by
two. That would look like this: (180-x)/2. If you further simplify it, you get
90-x/2. That is the angle measure of A and B. Since angle B and angle CBE form
a ninety degree angle, all you need to do is this: 90-(90-x/2) to get angle
CBE. What is left is x/2, the measure of angle CBE. 90-x/2 added to x/2 make
90 degrees.
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12/2/08 5:46 PM
The angle measure of CBE will always be a variable :x/2. That's because it
can be any positive number. I tried substituting 3 angle measures for x. I
first did 90 degrees. If x was 90 degrees, angle CBE would be 45, congruent to
angle B (they both add up to a 90 degree angle). If x was 60 degrees, angle
CBE would be 30. If x was 10 degrees, then angle CBE would be 5 degrees. As
long as the number is positive, angle CBE equals x/2 degrees.
Answer #7603:
From: 3730
School: 22
The measure of angle CBE=measure EBA-measure CBA.
a = angle
(a BAC+aX+aCBA=180 degrees)
aCBA=180-aX-aBAC
aCBE=aEBA-aCBA
aCBA congruent to aBAC because it is an isosceles triangle.
Don't forget the Base Angles Theorem which states If two sides of a
triangle are congruent, then the angles opposite them are congrunet.
This theorem helps you.
Answer #7604:
From: 1252
School: 62
90-(180-x)/2
Since AC and BC are equal then CAB and ABC are also equal. The angles
CAB and ABC plus X equal 180. Therefore using a given X, first solve
for ABC using the formula (180-x)/2, then subtract the resulting
amount for ABC from 90 (the right angle ABE)to arrive at CBE.
For instance if X were 60, then the angle CBE would equal 30.
Answer #7605:
From: 1646
School: 490
The measure of angle CBE will be X/2.
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12/2/08 5:46 PM
First i started off by asking my self what the 2 abgles at the bottom of
triangle ABC would measure. Because it was given that AC=CB that would mean
that triangle ABC was isoscoles and because of that then the base angle would
be =. Since the measure of the 3 angles of a triangle add up to 180 i made the
2 base angles equal (180-X)/2 i subtracted x from 180 so i would know how much
the other 2 angles would add up to and since they are = then i divided by 2.
so the measure of angle ABC would be (180-X)/2. angle ABC and angle CBE would
add up to 90 because angle ABE and DBE from a linear pair and since angle EBD
is 90 then angle ABE is also 90. if angle ABE is 90 then angle ABC and CBE add
up to 90. so angle CBE would equal 90-[(180-x)/2] i solved it and i ended up
with X/2.
Answer #7607:
From: 3961
School: 229
The measure of angleCBE is 1/2x.
The perpendicular bisector of angleACB is parrallel to the line BE.
The transversal is CB and since the lines are parrallel they form
alternate interior angles. 1/2x is the alternate interior angle for
angleCBE. The answer is 1/2x equals the measure of angleCBE.
Answer #7608:
From: 667
School: 21
If the measure of angle ACB is x, then the measure of angle CBE is x/2
I know that CA is congruent to CB. If two sides of a triangle are
congruent, then it is an isosceles triangle, and the base angles (in
this case angles CAB and CBA) are congruent. The sum of the angles of
a triangle is 180, so the sum of the two base angles is 180-x, and
because they have equal measurements, they each are (180-x)/2. It is
given that angle EBD is a right angle. Angle EBA is supplementary to
angle EBD, and supplements of right angles are right angles, so angle
EBA is a right angle, measureing 90 degrees. To find angle EBC, the
measurement of angle CBA should be subtracted from the measurement of
angle EBA. 90-(180-x)/2 reduces to x/2, so the measurement of angle
EBC is x/2.
Answer #7609:
From: 3170
School: 800
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12/2/08 5:46 PM
The angle of CBE is the same as angle X.
The reason this is the case is because of the opposite interior angle rule.
Answer #7611:
From: 1761
School: 18
(180-x)
90- -----2
CA=CB, therefore <A=<CBA. Triangle CAB is an isosceles because two
sides are congruent. In any triangle, the angles added up together
equals 180 degrees. If you subtract x from 180 you will get <A+<ABC.
Since they are congruent, you divide 180-x by two and you will get <
ABC. Because EB is perpendicular to AD, <EBA is a right angle. If you
subtract <ABC from <EBA (90-[180-x/2], you will get the m<EBC.
Answer #7614:
From: 2757
School: 13
If the measure of angle ACB is x degrees, the measure of angle CBE is
x/2.
The first step I did was fill in the given information:
"AC = BC"
"angle EBD is a right angle (90 degrees)"
"the measure of angle ACB is x degrees"
The using the first of the 3 givens (AC is conguent to BC), I knew
the opposite angles are conguent as well (angle CAB is congruent to
angle CBA)
The sum of the interior angles ALWAYS adds up to 180 degrees. Angle
ACB is X degrees
Therefore, the sum of angles CAB and CBA can be expressed as (180x)/2 (/2 because they are conguent)
To make matters simpler, I called the measure of angle CBE, y.
The second of the 3 givens stated angle EBD is a right angle, and
therefore is 90 degrees. We can assume from the diagram that ABD is
a straight line, and therefore is 180 degrees.
Now, we have all the data neccessery for setting up an equation.
will add all the three angles and have them equal 180 degrees:
I
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12/2/08 5:46 PM
CBA + CBE + EBD = 180
(180-x)/2 + y + 90 = 180
solving for y interms of x, I get:
y=x/2
y represented the measure of angle CBE.
If the measure of angle ACB is x degrees, the measure of angle CBE is
x/2.
Thank you!
Shai Dardashti
Akiba Hebrew Academy
[email protected]
Answer #7620:
From: 3073
School: 927
Angle C measures .5x degrees.
Clearly, since the base angles are congruent in an icosceles triangle
and all three angles in a triangle sum up to 180, the measure of angle
CBA is (180-x)/2, or 90 - .5x. Also, since angle EBD is right, EB is
perpendicular to BD, making angle EBA right as well. Therefore,
angles CBA and CBE are congruent, making the measure of angle CBE 90 (90 - .5x) = .5x.
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