Download - Angle Pair Relationship
Angle Pair RelationshipLesson 1.6
Thursday, April 9, 2020
Angle Pair Relationship
• angles sharing a common side and vertex but no common interior points
Illustration:A
B
C
D
●
●
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ABC and CBD are adjacent angles
Adjacent Angles
Angle Pair Relationship
• two angles are complementary if and only if the sum of the degree measure is 90.
Illustration:A
DE
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●●
460
M
A E
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● ●440
EDA + MAE = 900
Complementary Angles
Angle Pair Relationship
• two angles are supplementary if and only if the sum of the degree measure is 180.
Illustration:A
DE
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460M
A E
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● ●1340
EDA + MAE = 1800
Supplementary Angles
Angle Pair Relationship
Complementary and Supplementary
Complementary and supplementaryangles can be adjacent angles or non-adjacent angles
Angle Pair Relationship
Complementary and Supplementary
Example
In the figure, name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles.
ANSWER Complementary angles
Supplementary angles
Adjacent angles
BAC and RST
CAD and RST
BAC and CAD
In the figure, name a pair of complementary
angles, a pair of supplementary angles, and a
pair of adjacent angles.
1.
Are KGH and LKG adjacent angles ? Are FGK and FGHadjacent angles? Explain.
2.
Angle Pair Relationship
Complementary and Supplementary
Try it yourself!
1. FGK and GKL,
HGK and GKL,
FGK and HGK
ANSWER
2. No, they do not share a common vertex.
No, they have common interior points.
Angle Pair Relationship
Find Complement and Supplement
Example
a.) Given that 1 is a complement of 2 and m 1 = 68°, find m 2
b.) Given that 3 is a supplement of 4 and m 4 = 56°, find m 3
m 1Answer + m 2 = 900 then m 2 = 220
m 3Answer + m 4 = 1800 then m 3 = 1240
Angle Pair Relationship
Complementary and Supplementary
Try it yourself!
3.) Given that 1 is a complement of 2 and m 2 = 8°, find m 1
4.) Given that 3 is a supplement of 4 and m 3 = 117°, find m 4
5.) LMN and PQR are complementary angles. Find the measures of the angles if mLMN = (4x – 2)0 and mPQR = (9x + 1)0
= 820
= 630
= 260, 640
Angle Pair Relationship
• two angles form a linear pair if and only if they are adjacent and their sides form a straight angle or opposite rays.
Illustration:
A B
C
D● ●
●
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ABC and CBD are linear pair
Linear Pair Angles
Angle Pair Relationship
• two angles are vertical if the sides form two opposite rays
Illustration:
1 and 2 are vertical angles
1
2
3 4
3 and 4 are vertical angles
vertical angles are congruent
Vertical Angles
Angle Pair RelationshipLinear Pair and Vertical Angles
Identify all of the linear pairs and all of the vertical angles in the figure at the right.
Example
Linear pair angleAnswer 1 and 4
4 and 5
Vertical angle 1 and 5
Angle Pair RelationshipLinear Pair and Vertical Angles
Example
Two angles form a linear pair. The measure of one angle is 5 times the measure of the other. Find the measure of each angle.
Solution Let x° be the measure of one angle. The measure of the other angle is 5x°.
x + 5x = 1800 then x = 300
The measure of the angles are 300
and 1500
Answer
Angle Pair RelationshipLinear Pair and Vertical Angles
Try it yourself!
6.) Do any of the numbered angles in the diagram below form a linear pair? Which angles are vertical angles? Explain.
7.) The measure of an angle is twice the measure of its complement. Find the measure of each angle.
Linear pair angle : noneAnswer
Vertical angle: 1 and 4 2and 5 3and 6
The measure of the angles are 300
and 600
Answer
Angle Pair RelationshipUse the figure to solve problem 1-3
1. m 1= 3x, m 2=x, m EBD=104.
Find x, m 1 and m 2
2. BD bisects ABC, m2=5x – 3, m 3=2x+30. Find x m 2
x = 26, m1 = 78 and m2 = 26
x = 11, m2 = 52
A
B
C
D
E•
•
•
•
•
1 2
3
3. mEBC = 136 m1=93, m 2=20. Find m 3
m3 = 23
4.) Use the figure on the right to find the x and y.
x = 225x -7 3x + 11
y = 35 2y + 7