1.5 –Describe Angle Pair Relationships
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Transcript of 1.5 –Describe Angle Pair Relationships
1.5 –Describe Angle Pair Relationships
Adjacent angles: Two angles that share a common side and vertex
12
1 is adjacent to 2
Complementary Angles: Two angles that add to 90°
m1 + m2 = 90°
12 1
2
Supplementary Angles: Two angles that add to 180°
m1 + m2 = 180°
1 2
1
2
Linear Pair: Two adjacent angles whose noncommon sides are opposite rays
1 2
They will always add to 180°
m1 + m2 = 180°
Vertical Angles: Two angles whose sides form two pairs of opposite rays
12
They will always be congruent!
21
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 .
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
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
3. 1 and 2 are complementary angles. Given the measure of 1, find m2.
m1 = 82°
m2 = 8°90 – 82 =
3. 1 and 2 are complementary angles. Given the measure of 1, find m2.
m2 = 67°90 – 23 =
m1 = 23°
4. 1 and 2 are supplementary angles. Given the measure of 1, find m2.
m2 = 98°180 – 82 =
m1 = 82°
m2 = 75°180 – 105 =
m1 = 105°
4. 1 and 2 are supplementary angles. Given the measure of 1, find m2.
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°
5. Find the measure of ABD and DBC.
2x + 3x = 90
5x = 90x = 18
mABD = 2(18)= 36°
mDBC = 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.
16x + 9x + 5 = 180
25x + 5 = 18025x = 175
x = 7°
16x + 4y = 180
16(7) + 4y = 180
112 + 4y = 180
4y = 68y = 17°
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°
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°
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