Presentation on theme: "Ch 2 Sect 3 Complementary and Supplementary Angles Complementary Angles have measures that add up to 90°. Supplementary Angles have measures that add up."— Presentation transcript:
Ch 2 Sect 3 Complementary and Supplementary Angles Complementary Angles have measures that add up to 90°. Supplementary Angles have measures that add up to 180°.
Ch 2 Sect 3 Complementary and Supplementary Angles Adjacent Angles share a vertex and a side but do not share any interior points. (next-door neighbors )
Example 1 Identify Complements and Supplements Determine whether the angles are complementary, supplementary, or neither. a. b. c. SOLUTION a. Because 22° + 158° = 180°, the angles are supplementary. b. Because 15° + 85° = 100°, the angles are neither complementary nor supplementary. c. Because 55° + 35° = 90°, the angles are complementary.
Checkpoint Identify Complements and Supplements ANSWER supplementary ANSWER complementary Determine whether the angles are complementary, supplementary, or neither. 1. ANSWER neither 2. 3.
Example 3 Measures of Complements and Supplements A is a complement of C, and m A = 47°. Find m C. a. b. P is a supplement of R, and m R = 36°. Find m P. SOLUTION a. A and C are complements, so their sum is 90°. b. P and R are supplements, so their sum is 180°. m A + m C = 90°m P + m R = 180° 47° + m C = 90°m P + 36° = 180° 47°+ m C – 47° = 90° – 47°m P + 36° – 36° = 180° – 36° m C = 43° m P = 144°
Checkpoint Measures of Complements and Supplements B is a complement of D, and m D = 79°. Find m B G is a supplement of H, and m G = 115°. Find m H. ANSWER 11° ANSWER 65°
Example 2 Identify Adjacent Angles Tell whether the numbered angles are adjacent or nonadjacent. SOLUTION a. Because the angles do not share a common vertex or side, 1 and 2 are nonadjacent. b. Because the angles share a common vertex and side, and they do not have any common interior points, 3 and 4 are adjacent. c. Although 5 and 6 share a common vertex, they do not share a common side. Therefore, 5 and 6 are nonadjacent. a. b.c.
Ch 2 Sect 3 3k k Find k.
Ch 2 Sect 3 1.Name a straight angle. 2.Name 2 congruent supplementary angles. 3.Name 2 angles that are supplementary but not congruent. 4.Name 2 complementary angles.