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1.5 –Describe Angle Pair Relationships
Adjacent angles: Two angles that share a
common side and vertex
2 1
1 is adjacent to 2
Complementary Angles: Two angles that
add to 90°
1
2
1
2
m1 + m2 = 90°
Supplementary Angles: Two angles that
add to 180°
1
2
1
m1 + m2 = 180°
2
Linear Pair: Two adjacent angles whose
noncommon sides are opposite
rays
1
2
They will always add to 180°
m1 + m2 = 180°
Vertical Angles: Two angles whose sides form
two pairs of opposite rays
1
2
They will always be congruent!
1  2
1. Tell whether the indicated angles are adjacent.
EFG and HGF
no
1. Tell whether the indicated angles are adjacent.
JNM and MNK
yes
2. Name a pair of complementary angles, supplementary
angles, and vertical angles .
Vertical:
ROL  NOP
L
M
R
N
O
Q
P
LOM  QOP
Complementary:
mQOR + mROL = 90
mMON + mNOP = 90
Supplementary:
mROL + mLON = 180
mROM + mMON = 180
mQOL + mLOM = 180
2. Name a pair of complementary angles, supplementary
angles, and vertical angles .
Vertical:
DGE  BGC
A
EGB  DGC
E
D
Complementary:
B mDGE + mEGA = 90
G
C
Supplementary:
mDGE + mEGB = 180
mDGA + mAGB = 180
mEGA + mAGC = 180
3. 1 and 2 are complementary angles. Given the
measure of 1, find m2.
m1 = 82°
m2 = 90 – 82 = 8°
3. 1 and 2 are complementary angles. Given the
measure of 1, find m2.
m1 = 23°
m2 = 90 – 23 = 67°
4. 1 and 2 are supplementary angles. Given the
measure of 1, find m2.
m1 = 82°
m2 = 180 – 82 = 98°
4. 1 and 2 are supplementary angles. Given the
measure of 1, find m2.
m1 = 105°
m2 = 180 – 105 = 75°
5. Find the measure of ABD and DBC.
4x + 6 + 11x – 6 = 180
15x = 180
x = 12
mABD = 4(12)+6
= 48+6
= 54°
mDBC = 11(12)-6
= 132-6
= 126°
5. Find the measure of ABD and DBC.
2x + 3x = 90
5x = 90
x = 18
mABD = 2(18)
= 36°
mDBC = 3(18)
= 54°
6. Use the diagram below. Tell whether the angles are
vertical angles, linear pair, or neither.
1 and 2
Linear pair
6. Use the diagram below. Tell whether the angles are
vertical angles, linear pair, or neither.
1 and 3
Vertical angles
6. Use the diagram below. Tell whether the angles are
vertical angles, linear pair, or neither.
2 and 4
Vertical angles
6. Use the diagram below. Tell whether the angles are
vertical angles, linear pair, or neither.
5 and 7
neither
6. Use the diagram below. Tell whether the angles are
vertical angles, linear pair, or neither.
5 and 8
neither
7. Find the values of x and y.
6x – 11 + 2x – 9 = 180
8x – 20 = 180
8x = 200
x = 25°
20y + 19 + 2x – 9 = 180
20y + 19 + 2(25) – 9 = 180
20y + 60 = 180
20y = 120
y = 6°
7. Find the values of x and y.
21x – 3 + 5x + 1 = 180
26x – 2 = 180
26x = 182
x = 7°
4y + 17y – 9 = 180
21y – 9 = 180
21y = 189
y = 9°
HW Problem
Section Page #
1.5
Assignment
38-41 4, 5, 7, 11, 15-19 odd, 29-33 odd, 50, 61
# 50 Vertical angles
Ans:
ex: AGB & EGD
Spiral ?s
14-15