1.5 –Describe Angle Pair Relationships
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Transcript of 1.5 –Describe Angle Pair Relationships
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1.5 –Describe Angle Pair Relationships
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Adjacent angles: Two angles that share a common side and vertex
12
1 is adjacent to 2
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Complementary Angles: Two angles that add to 90°
m1 + m2 = 90°
12 1
2
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Supplementary Angles: Two angles that add to 180°
m1 + m2 = 180°
1 2
1
2
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Linear Pair: Two adjacent angles whose noncommon sides are opposite rays
1 2
They will always add to 180°
m1 + m2 = 180°
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Vertical Angles: Two angles whose sides form two pairs of opposite rays
12
They will always be congruent!
21
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1. Tell whether the indicated angles are adjacent.
EFG and HGF
no
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1. Tell whether the indicated angles are adjacent.
JNM and MNK
yes
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2. Name a pair of complementary angles, supplementary angles, and vertical angles .
Complementary:QOR and ROL
Supplementary:ROL and LON
ROM and MON
Vertical:
L
M
N
PQ
R O
MON and NOP
QOL and LOM
ROL and NOP
LOM and QOP
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2. Name a pair of complementary angles, supplementary angles, and vertical angles .
Complementary:DGE and EGA
Supplementary:DGE and EGB
DGA and AGB
Vertical:
EGA and AGC
DGE and BGC
EGB and DGC
A
B
C
D
E
G
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3. 1 and 2 are complementary angles. Given the measure of 1, find m2.
m1 = 82°
m2 = 8°90 – 82 =
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3. 1 and 2 are complementary angles. Given the measure of 1, find m2.
m2 = 67°90 – 23 =
m1 = 23°
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4. 1 and 2 are supplementary angles. Given the measure of 1, find m2.
m2 = 98°180 – 82 =
m1 = 82°
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m2 = 75°180 – 105 =
m1 = 105°
4. 1 and 2 are supplementary angles. Given the measure of 1, find m2.
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5. Find the measure of ABD and DBC.
4x + 6 + 11x – 6 = 180
15x = 180x = 12
mABD = 4(12)+6= 48+6= 54°
mDBC = 11(12)-6= 132-6= 126°
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5. Find the measure of ABD and DBC.
2x + 3x = 90
5x = 90x = 18
mABD = 2(18)= 36°
mDBC = 3(18)= 54°
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6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.
1 and 2
Linear pair
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6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.
1 and 3
Vertical angles
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6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.
2 and 4
Vertical angles
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6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.
5 and 7
neither
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6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.
5 and 8
neither
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7. Find the values of x and y.
16x + 9x + 5 = 180
25x + 5 = 18025x = 175
x = 7°
16x + 4y = 180
16(7) + 4y = 180
112 + 4y = 180
4y = 68y = 17°
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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 = 120y = 6°
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7. Find the values of x and y.
9x + 2 + 10x + 7 = 180
19x + 9 = 18019x = 171
x = 9°
18y + 25 + 9x + 2 = 180
18y + 25 + 9(9) + 2 = 180
18y + 108 = 180
18y = 72y = 4°
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HW Problem
# 49
1.5 38-41 1-5, 7-33 odd, 39-43 odd, 49-53, 61, 62
Ans:
ex: FGA & AGC
supplementary**Bring calculator tomorrow