2.3 Complementary and Supplementary Angles 10/2/07 Complementary angles – the sum of two angles is 90°. Each angle is the complement of the other. Angle A and Angle B are complementary angles. A 32° B 58°

Supplementary Angles Supplementary Angles – the sum of two angles is 180°. Each angle is the supplement of the other. Angle C and Angle D are supplementary angles. C 134° D 46°

Identify Complements and Supplements Determine whether the angles are complementary, supplementary, or neither. a. a. Because 22° + 158° = 180°, the angles are supplementary. 22°158°

Identify Complements and Supplements Determine whether the angles are complementary, supplementary, or neither. b. b. Because 15° + 85° = 100°, the angles are neither complementary or supplementary. 15° 85°

Identify Complements and Supplements Determine whether the angles are complementary, supplementary, or neither. c. c. Because 55° + 35° = 90°, the angles are complementary. 35° 55°

Adjacent Angles Two angles are adjacent angles if they share a common vertex and side, but have no common interior points. and are adjacent angles. 1 2 Common side Common Vertex

Adjacent Angles Tell whether the numbered angles are adjacent or nonadjacent. a. a.Because the angles do not share a common vertex or a common side, then andare nonadjacent. 1 2

Adjacent Angles Tell whether the numbered angles are adjacent or nonadjacent. b. Because the angles share a common vertex and a common side, and they do not have an common interior points, and are adjacent. 3 4

Adjacent Angles Tell whether the numbered angles are adjacent or nonadjacent. c. Although and share a common vertex, they do not share a common side. Therefore, and are nonadjacent. 5 6

Measures of Complements and Supplements a. is a complement of, and Find b. is a supplement of,and Find

Measures of Complements and Supplements SOLUTION! a. and are complements, so their sum is 90°

Measures of Complements and Supplements SOLUTION! b. and are supplements, so their sum is 180°