1. 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.

2. 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.

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.

4. 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 °

5. 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 SOLUTION

6. GUIDED PRACTICE for Examples 2 and 3 3. Given that 1 is a complement of 2 and m 2 = 8 o, find m 1. 82 o ANSWER 4. Given that 3 is a supplement of 4 and m 3 = 117 o, find m 4. 63 o ANSWER 5. LMN and PQR are complementary angles. Find the measures of the angles if m LMN = (4x – 2) o and m PQR = (9x + 1) o. ANSWER 26 o, 64 o