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1.6 Angle Pair Relationships
GOAL 1 Identify vertical angles and linear pairs.
GOAL 2 Identify complementary and supplementary angles.
What you should learn
To solve real-life problems, such as finding the measures of angles formed by the cables of a bridge.
Why you should learn it
GOAL 1 VERTICAL ANGLES AND LINEAR PAIRS
1.6 Angle Pair Relationships
Vocabulary
Two angles whose sides form two pairs of opposite rays are called _____________. vertical angles
14 23
Identify the pairs of vertical angles in the diagram.
Click to check.
1 and 3 2 and 4
Two adjacent angles whose noncommon sides are opposite rays are called a _________.linear pair
5 6
common side
noncommon sides
5 and 6 are a linear pair.
EXAMPLE 1
Extra Example 1
EXAMPLE 2
1 5 432
a. Are a linear pair?
b. Are a linear pair?
c. Are vertical angles?
d. Are vertical angles?
Click to see the answers.
1 and 2
5 and 3
4 and 5
1 and 3
yes
no
no
yes
Extra Example 2In one town, Main Street and Columbus Avenue intersect to form an angle of 36°. Find the measures of the other three angles.
Click to see a diagram.
Columbus Avenue
Main Street36°m X
m Y m Z
Click to see the answers.
144
36 144
EXAMPLE 3
Extra Example 3
Solve for x and y. Then find the angle measures.
Click for a hint.
L
M
PN
O
(4 15) x(5 30) x
(3 15) y(3 15) y
180
and 180
m LPM m NPM
m LPO m NPO
Solve each equation to find x and y. Click for the answers.
15, 30 x y m LPM m OPN
m MPN m LPO
75
105
Checkpoint
1. Name one pair of vertical angles and one pair of angles that form a linear pair. Click to see the answers.
J
H
K
GI
(5 30) x(2 4) x
Vertical angle pairs:
Linear pairs:
and ; and IHJ GHK JHK GHI
and ; and ;
and ; and
IHJ JHK JHK KHG
KHG GHI GHI IHJ
2. What is the measure of ?GHI 140
GOAL 2 COMPLEMENTARY AND SUPPLEMENTARY ANGLES
1.6 Angle Pair Relationships
Vocabulary
If the sum of the measures of two angles is 90°, the angles are ______________ angles, and each is the ___________ of the other.
complementarycomplement
21
Note: Complementary angles may or may not be adjacent.
are nownonadjacent complementary angles.
1 and 2
If the sum of the measures of two angles is 180°, the angles are _____________ angles, and each is the ___________ of the other.
EXAMPLE 4
supplementarysupplement
3 4
Note: Supplementary angles may or may not be adjacent.If are adjacent and supplementary, they form a _________.
3 and 4 linear pair
are now nonadjacent supplementary angles, and they no longer form a linear pair.
3 and 4
Extra Example 4
EXAMPLE 5
State whether the two angles are complementary, supplementary, or neither. Click for the solution.
12
39
6
12
39
6
neithersupplementary
neither
Extra Example 5a. Given that is a supplement of
find G , and is 82 , H m G
.m H
Click to see the solution.
U , and is 73 , V m U.m V
b. Given that is a complement of find
Click to see the solution.
180 m G m H82 180 m H
98 m H
90 m U m V
73 90 m V
17 m V
EXAMPLE 6
Extra Example 6
are supplementary. The measure of is half the measure of Find Click for a hint.
and ST T.S .m S
1180 and
2m T m S m T m S
Substitute and solve. Click for the solution.
180m T m S 1
1802m S m S
3180
2m S
120m S
Checkpoint are complements and are supplements. If is four times find the measure of each of the three angles. Click for a hint.
and D E and D F m E ,m D
4( ) and 90m E m D m E m D
Substitute and solve. Click for the answers.
m D
m E
m F
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