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

●

●

●

●

ABC and CBD are adjacent angles

Adjacent Angles


• two angles are complementary if and only if the sum of the degree measure is 90.

Illustration:A

DE

●

●●

460

M

A E

●

● ●440

EDA + MAE = 900

Complementary Angles


• two angles are supplementary if and only if the sum of the degree measure is 180.

Illustration:A

DE

●

●●

460M

A E

●

● ●1340

EDA + MAE = 1800

Supplementary Angles


Complementary and Supplementary

Complementary and supplementaryangles can be adjacent angles or non-adjacent angles



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.



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.


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



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


• 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● ●

●

●

ABC and CBD are linear pair

Linear Pair Angles


• 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


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


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

angle pair relationship

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