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EXAMPLE 1

In the figure, name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles. Because 32 ° + 58 ° = 90 ° , BAC and RST are complementary angles. Because 122° + 58° = 180° , CAD and RST are supplementary angles.

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EXAMPLE 1

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  1. In the figure, name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles. Because 32°+ 58° = 90°, BACand RSTare complementary angles. Because 122° + 58° = 180°,CADand RSTare supplementary angles. Because BACand CADshare a common vertex and side, theyare adjacent. EXAMPLE 1 Identify complements and supplements SOLUTION

  2. In the figure, name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles. 1. ANSWER FGK and GKL, HGKandGKL, FGKandHGK for Example 1 GUIDED PRACTICE

  3. Are KGHand LKGadjacent angles ? Are FGKand FGHadjacent angles? Explain. 2. ANSWER No, they do not share a common vertex. No, they have common interior points. for Example 1 GUIDED PRACTICE

  4. Given that 1 is a complement of 2 and m1 = 68°, • find m2. 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 SOLUTION

  5. m 3 = 180° – m 4 = 180° –56° = 124° b. Given that 3 is a supplement of 4and m 4=56°, find m3. b.You can draw a diagram with supplementary adjacent angles to illustrate the relationship. EXAMPLE 2 Find measures of a complement and a supplement SOLUTION

  6. 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 Sports

  7. 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.

  8. STEP2 Evaluate: the original expressions when x = 34. m ECD = (x + 2)° = ( 34 + 2)° = 36° m BCE = (4x + 8)° = (4 34 + 8)° = 144° ANSWER The angle measures are144°and36°. EXAMPLE 3 Find angle measures SOLUTION

  9. 3. Given that 1 is a complement of 2 and m2 = 8o, find m1. ANSWER ANSWER 82o 63o 4. Given that 3 is a supplement of 4 and m3 = 117o, find m4. 5. LMNand PQRare complementary angles. Find the measures of the angles if m LMN= (4x –2)o and m PQR = (9x + 1)o. ANSWER 26o, 64o for Examples 2 and 3 GUIDED PRACTICE

  10. Identify all of the linear pairs and all of the vertical angles in the figure at the right. ANSWER 1 and 5 are vertical angles. 1 and 4 are a linear pair. 4 and 5 are also a linear pair. ANSWER EXAMPLE 4 Identify angle pairs SOLUTION To find vertical angles, look or angles formed by intersecting lines. To find linear pairs, look for adjacent angles whose noncommon sides are opposite rays.

  11. ALGEBRA Two angles form a linear pair. The measure of one angle is 5 times the measure of the other. Find the measure of each angle. Let x° be the measure of one angle. The measure of the other angle is 5x°. Then use the fact that the angles of a linear pair are supplementary to write an equation. EXAMPLE 5 Find angle measures in a linear pair SOLUTION

  12. The measures of the angles are 30oand 5(30)o = 150o. ANSWER EXAMPLE 5 Find angle measures in a linear pair xo+ 5xo = 180o Write an equation. 6x = 180 Combine like terms. x = 30o Divide each side by 6.

  13. 6. Do any of the numbered angles in the diagram below form a linear pair? Which angles are vertical angles? Explain. ANSWER No, no adjacent angles have their noncommon sides as opposite rays, 1 and 4 , 2 and 5,3 and 6, these pairs of angles have sides that from two pairs of opposite rays. For Examples 4 and 5 GUIDED PRACTICE

  14. 60°, 30° ANSWER For Examples 4 and 5 GUIDED PRACTICE 7. The measure of an angle is twice the measure of its complement. Find the measure of each angle.

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