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° –

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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. m  BCE + m  ECD = 180°

EXAMPLE 3 Find angle measures STEP 2 Evaluate: the original expressions when x = 34. m BCE = (4x + 8)° = ( )° = 144° m ECD = (x + 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 1 2 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 °

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°