# Complementary Angles have measures that add up to 90°.

## Presentation on theme: "Complementary Angles have measures that add up to 90°."— Presentation transcript:

Complementary Angles have measures that add up to 90°.
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°. 1

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 ) 2

Because 22° + 158° = 180°, the angles are supplementary.
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. 3

Checkpoint Identify Complements and Supplements Determine whether the angles are complementary, supplementary, or neither. 1. ANSWER neither 2. ANSWER complementary 3. ANSWER supplementary

A is a complement of C, and mA = 47°. Find mC. a.
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° 5

B is a complement of D, and mD = 79°. Find mB. 4.
Checkpoint Measures of Complements and Supplements B is a complement of D, and mD = 79°. Find mB. 4. ANSWER 11° 5. G is a supplement of H, and mG = 115°. Find mH. ANSWER 65°

Example 2 Identify Adjacent Angles Tell whether the numbered angles are adjacent or nonadjacent. a. b. c. 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. 7

Ch 2 Sect 3 Find k. 2k 3k + 10

Ch 2 Sect 3 Name a straight angle. Name 2 congruent supplementary angles. Name 2 angles that are supplementary but not congruent. Name 2 complementary angles.

Ch 2 Sect 3 Homework: Page #1-24 and #35