EXAMPLE 2 Find measures of a complement and a supplement

SOLUTION

a. Given that 1 is a complement of 2 and m 1 = 68°, find m 2.

m 2 = 90° – m 1 = 90° – 68° = 22

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

EXAMPLE 2 Find measures of a complement and a supplement

b. You can draw a diagram with supplementary adjacent angles to illustrate the relationship. m 3 = 180° – m 4 = 180° –56° = 124°

SOLUTION

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

EXAMPLE 3 Find angle measures

Sports

When viewed from the side, the frame of a ball-return net forms a pair of supplementary angles with the ground. Find m BCE and m ECD.

SOLUTION

EXAMPLE 3 Find angle measures

STEP 1 Use the fact that the sum of the measures of supplementary angles is 180°.

Write equation.

(4x+ 8)° + (x + 2)° = 180° Substitute.

5x + 10 = 180 Combine like terms.

5x = 170

x = 34

Subtract 10 from each side.

Divide each side by 5.

mBCE + m ∠ECD = 180°

EXAMPLE 3 Find angle measures

STEP 2

Evaluate: the original expressions when x = 34.

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

m ECD = (x + 2)° = ( 34 + 2)° = 36°

The angle measures are 144° and 36°.ANSWER

GUIDED PRACTICE for Examples 2 and 3

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

m 1 = 90° – m 2 = 90°– 8° = 82°

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

SOLUTION

12 8°

GUIDED PRACTICE for Examples 2 and 3

4. Given that 3 is a supplement of 4 and m 3 = 117°, find m 4.

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

m 4 = 180° – m 3 = 180°– 117° = 63°

SOLUTION

3 4117°

GUIDED PRACTICE for Examples 2 and 3

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

m LMN + m PQR = 90°

(4x – 2 )° + ( 9x + 1 )° = 90°

13x – 1 = 90

13x = 91

x = 7

Complementary angle

Substitute value

Combine like terms

Add 1 to each side

Divide 13 from each side

SOLUTION

GUIDED PRACTICE for Examples 2 and 3

Evaluate the original expression when x = 7

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

m PQR = (9x – 1 )° = (9·7 + 1)° = 64°

ANSWER m LMN = 26° m PQR = 64°