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a. You can draw a diagram with complementary adjacent angles to illustrate the relationship. m 2 = 90° – m 1 = 90° – 68° = 22. EXAMPLE 2. Find measures of a complement and a supplement. Given that 1 is a complement of 2 and m 1 = 68° , find m 2 .

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a.You can draw a diagram with complementary adjacent angles to illustrate the relationship.

m 2 = 90° – m 1 = 90° – 68° = 22

EXAMPLE 2

Find measures of a complement and a supplement

  • Given that 1 is a complement of 2 and m1 = 68°,

  • find m2.

SOLUTION


b. You can draw a diagram with supplementary adjacent angles to illustrate the relationship.

m 3 = 180° – m 4 = 180° –56° = 124°

b. Given that 3 is a supplement of 4and m 4=56°,

find m3.

EXAMPLE 2

Find measures of a complement and a supplement

SOLUTION


Sports

When viewed from the side, the frame of a ball-return net forms a pair of supplementary angles with the ground. Find mBCEand mECD.

EXAMPLE 3

Find angle measures


Use the fact that the sum of the measures of supplementary angles is 180°.

STEP1

mBCE+m∠ ECD=180°

EXAMPLE 3

Find angle measures

SOLUTION

Write equation.

(4x+ 8)°+ (x +2)°= 180°

Substitute.

5x + 10 = 180

Combine like terms.

5x = 170

Subtract10 from each side.

x = 34

Divide each side by 5.


STEP angles is 2

Evaluate: the original expressions when x = 34.

m BCE = (4x + 8)° = (4 34 + 8)° = 144°

m ECD = (x + 2)° = ( 34 + 2)° = 36°

ANSWER

The angle measures are144°and36°.

EXAMPLE 3

Find angle measures


3. angles is Given that 1 is a complement of 2 and m2 = 8° , find m1.

m 1 = 90° – m 2 = 90°– 8° = 82°

1

2

for Examples 2 and 3

GUIDED PRACTICE

SOLUTION

You can draw a diagram with complementary adjacent angle to illustrate the relationship


4. angles is Given that 3 is a supplement of 4 and m3 = 117°, find m4.

m 4 = 180° – m 3 = 180°– 117° = 63°

117°

3

4

for Examples 2 and 3

GUIDED PRACTICE

SOLUTION

You can draw a diagram with supplementary adjacent angle to illustrate the relationship


m LMN + m PQR angles is = 90°

for Examples 2 and 3

GUIDED PRACTICE

5.LMNand PQRare complementary angles. Find the measures of the angles if m LMN= (4x –2)° and m PQR = (9x + 1)°.

SOLUTION

Complementary angle

(4x – 2 )° + ( 9x + 1 )° = 90°

Substitute value

13x – 1 = 90

Combine like terms

13x = 91

Add 1 to each side

x = 7

Divide 13 from each side


m LMN angles is = (4x – 2 )° = (4·7 – 2 )° = 26°

m PQR = (9x – 1 )° = (9·7 + 1)° = 64°

m PQR

ANSWER

m LMN

= 64°

= 26°

for Examples 2 and 3

GUIDED PRACTICE

Evaluate the original expression whenx = 7


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