Download Problem Set #3

1.4 – Angle Addition
Angle - consists of ____ different __________. The rays are sides of the
angle. The shared endpoint is the __________ of the angle.
Problem Set #1
Postulate 3 – Protractor Postulate
Consider OB and a point A on one side of OB . The ray of the form OA can be matched one to one
with real numbers from 0 to 180. The measure of AOB is equal to the absolute value of the
difference between the real numbers for OA and OB .
Classifying angles:
0  mA  90
mA  90
90  mA  180
mA  180 
_____________
_____________
_____________
_____________
Problem Set #2
Name all of the angles in the diagram at the right
and classify the angles as either acute, obtuse, right,
or straight.
D
B
E
48
90
42
A
C
Postulate 4 – Angle Addition Postulate
Words – If P is in the interior of RST , then the measures of RST is equal to the sum of the
measures of RSP and PST .
Symbols – If P is in the interior of RST , then mRST  mRSP  mPST .
Problem Set #3
Given the following two angle measures,
find the missing angle measure:
C
G
mGRC  90
mCRP  12
mGRP  ?
mGRC  ?
mCRP  21
mGRP  113
mGRC  85
mCRP  ?
mGRP  108
mGRC  2 x  10  ?
mCRP  x  ?
mGRP  100
P
R
Angle Bisector
An Angle Bisector is a ray that divides an angle into two angles that are congruent.
Tip – Angle Bisector problems are similar to midpoint problems
Problem Set #3
Given that DB bisects CDA , find the measure of all the angle measures
mCDB  30
mBDA  _____
mCDA  _____
mCDB  23
mBDA  _____
mCDA  _____
C
C
B
mCDB  _____
mBDA  _____
mCDA  80
B
A
D
C
mCDB  _____
mBDA  _____
mCDA  57
C
B
mCDB  5x  8
mBDA  7 x
mCDA  _____
C
B
A
D
mCDB  5x
mBDA  _____
mCDA  6 x  16
C
B
D
A
D
A
D
B
A
D
A
1.5 – Angle Pair Relationships
Adjacent Angles share a common _____________ and _________ but have no common interior
angles.
Adjacent Angles
Nonadjacent Angles
Complementary & Supplementary Angles
Complementary Angles’ angle sum = __________. Supplementary Angles’ angle sum = __________.
Problem Set #1
Given that ABC and DBC are complementary. Find the measure of DBC if
A) mABC  34
B) mABC  44
C) mABC  12
Given that ABC and DBC are supplementary. Find the measure of DBC if
D) mABC  34
E) mABC  175
F) mABC  97
Problem Set #2
Given that ABC and DBC are complementary. Find the measure of DBC if
A) mABC  20
mDBC  2x  30
B) mABC  x  12
mDBC  2x  27
Given that ABC and DBC are supplementary. Find the measure of ABC if
C) mABC  3x  20
mDBC  70
D) mABC  6x
mDBC  3x  45
Problem Set #3
Linear Pair and Vertical Angles
Linear Pair – two adjacent angles whose noncommon sides are opposite rays
Tip – you can spot them as two adjacent angles that sit on the same line and are supplementary
Vertical Angles – two angles whose sides form two pairs of opposite angles
Tip – any time two lines intersect, two sets of vertical angles are formed that are congruent
Problem Set #4
Problem Set #5
Given:
m1  2x  5
m4  8x  25
4
1
3
2
Find:
x
m1
m4
Problem Set #6
Given:
m1  3 y
m4  y  20
1
2
5
Find:
y
m1
m4
Problem Set #7
3
4