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EXAMPLE 2

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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EXAMPLE 2

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  1. 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

  2. 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

  3. 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

  4. 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.

  5. STEP2 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

  6. 3. Given that 1 is a complement of 2 and m2 = 8° , find m1. m 1 = 90° – m 2 = 90°– 8° = 82° 1 8° 2 for Examples 2 and 3 GUIDED PRACTICE SOLUTION You can draw a diagram with complementary adjacent angle to illustrate the relationship

  7. 4. 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

  8. m LMN + m PQR = 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

  9. m LMN = (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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