Download Angle Relationships

Name
Class
Date
Angle Relationships
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itiil i'
Essential question: How can you use angle pairs to solue problems?
PTORE
Measuring and Describing Angles
B
\Mhen lines intersect, several angles are
formed. Use a ruler or straightedge to draw
a pair of intersecting lines. Label each
angle in order clockwise from
Use a protractor to find
each angle measure.
Angle
I to 4.
Angle Measure
1
2
3
4
c
\.4rhat can
you say about
mll
and
ml3?
Angles 1 and 3 are vertical angles. They are opposite one another. Vertical angles
have equal measures, no sides in common, and no common interior points.
\.44rat is
D
the other pair of vertical angles
\Mhat can you say about
ml|
in A ?
andml2? About ml2 andml3?
c
o
o
E
Angles I and2 and angles 2 and 3 are adjacent angles. They share a common vertex
and a common side.
IJ
o
s
.9
3
L=
.=
\Mhat are the two other pairs of adjacent angles in the figure?
E
f,
i
-o
.g
5
\&hat can you say about the sum of the degree measures of each pair of
c
c
o)
adjacent angles?
5
-
())
Two angles whose measures add up to lB0o are called supplementary angles.
Each pair of adjacent angles in the figure you made are
angles.
Two angles whose measures add up to g0o are called complemerrtary angles.
REFTECT
i 1,
Angles AandBaresupplementary.
Chapter
5
mlA:
775
B0".mlB =
Lesson
1
EXAM
P
tE
FindingAngle Measures
Find the measure of IEHF,
IEHF and
angles.
are
The sum of their measures is
:180
+
Write and solve
-- an equation to find mlEHF.
2x=
nIEHF =
TRY THIS!
2.
Write and solve an equation to find the value of 3x and mlJML.
nIJML:3x
=
e
use the figure. 5Q
1.
2.
3,
I
fru.
Name a pair of vertical angles.
Name
a
pair of adjacent angles.
@
Name a pair of supplementary angles.
I
ro
t
f
4.
Name a pair of complementary angles.
+
_=
f
I
D
5.
Angle SUTmeasures 90". lVhat is rnlQUM
5.
Angle RUNmeasures 51'. \Mhat is wISUR?
c
f,
c
q
T
f'
@
7.
8.
n
Two streets intersect. One of the angles formed measures 136'. The angles adjacent to the
136. angle each measure 2f . \.Alhat does x equal? \.4lhat is the degree measure of each of
these adjacent angles?
3
o
f
Error Analysis Iames claims that when two adjacent angles measure 90' together,
the two angles are supplementary. Explain why Iames is wrong.
Chapter
5
176
Lesson
1
Date
Additional Practice
Use the diagram to name each figure.
1. a right angle
2. two acute angles
3. two obtuse angles
4. a pair of complementary angles
5. three pairs of supplementary angles
c
o
Use the diagram to find each angle measure.
E
\ \n
&-.d
--a\J
.=
g
.9
...'E
|
4\
e'\-"
f
L
f
o
I
6. lf ml2:
1
10o. find
ml4.
7. lf m11 = no, find mZ3.
.=
F
=c
8. The diagram shows the intersection of three
l
I
(9
roadways on a map. Based on the diagram, what
should be the measure of IECD?
Chapter
5
177
Practice and Problem Solving
Frohlerm $olwin
Use the flag of the Bahamas to solve the problems.
1. Name a right angle in the flag.
G
2. Name a pair of comPlementarY
tl
,--.1
angles in the flag.
f
3. Name two acute angles in the flag.
4. Name a pair of suPPlementary
angles in the flag.
The diagram illustrates a ray of light being reflected off a
mirror. The angle of incidence is congruent to the angle of
reflection. Choose the letter for the best answer'
5. Name a pair of supplementary angles.
A
B
C
D
ICMA, IAMN,
INMB, I.AMB
1"NMC, IDMN
IAMN, INAID
4A^t^
lljrs ^+
{-r}
ln*id*nc*
angles.
F ZNMB, IBMD
G IAMN, INMB
J
f
rn!rr*r
=
I-AMD
c
f,
tr
g
B. Find the measure of 14.
F 650
G 350
ct3
D none
650
c
350
D 900
5
tr
o
H
J
6'
250
900
10. Find the measure of 13.
9. Find the measure of 11.
Chapter
-o
I
7. Which angle is congruentto 12?
A
B
o
f
=
ICMA, IDMB
At1
Bt4
x
3
6. Name a pair of comPlementarY
H ICMA,
:rnnio nf
refl*nti*n
cli
F 900
G 450
250
178
H
J
350
650
Practice and Problem Solving
f
l
@
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o
l