1.5 Complementary and Supplementary Angles
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The document primarily discusses various types of angles, specifically complementary and supplementary angles, along with exercises to identify and calculate them. It includes definitions, examples, and practice problems for recognizing angle relationships and determining missing angles. Additionally, it emphasizes concepts such as vertical angles and congruence through the congruent complements and supplements theorems.
1.5 Complementary and Supplementary Angles
- 1. WARM UP 1/22/13 Mark no school on 1/20/13. Identify the type of angle: 1.30°8. 60 ° 2.120 ° 9. 158 ° 3.180 ° 10. 80 ° 4.90 ° 5.72 ° 6.140 ° 7.116 °
- 2. Complementary Angles Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees. Example: These two angles are complementary. WHY????
- 3. These two angles can be "pasted" together to form a right angle!
- 4. Supplementary Angles Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees. Example: These two angles are supplementary. WHY???
- 5. These two angles can be "pasted" together to form a straight line!
- 6. Vertical Angles Pairs of Angle formed by the intersection of 2 lines. They are across from each other. How many pairs? Vertical angles are congruent!!!
- 7. Review State whether the following are acute, right, or obtuse. 1. 3. 5. acute obtuse right 2. 4. acute ? ? obtuse
- 8. Complementary and Supplementary Find the missing angle. 1. Two angles are complementary. One measures 65 degrees. Answer : 25 2. Two angles are supplementary. One measures 140 degrees. Answer : 40
- 9. Complementary and Supplementary Find the missing angle. You do not have a protractor. Use the clues in the pictures. 1. x 2. x 55 165 X=35 X=15
- 10. Vertical Angles Find the missing angle. You do not have a protractor. Use the clues in the pictures. X=58 x 58
- 11. Identify Complements and Supplements • Determine whether the angles are complementary, supplementary, or neither. a. 22° 158° a. Because 22° + 158° = 180°, the angles are supplementary.
- 12. • Determine whether the angles are complementary, supplementary, or neither. b. 15° 85° b. Because 15° + 85° = 100°, the angles are neither complementary or supplementary.
- 13. • Determine whether the angles are complementary, supplementary, or neither. c. 55° 35° c. Because 55° + 35° = 90°, the angles are complementary.
- 14. Example 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.
- 15. Checkpoint Identify Complements and Supplements Determine whether the angles are complementary, supplementary, or neither. 1. ANSWER neither 2. ANSWER complementary 3. ANSWER supplementary
- 16. • Tell whether the numbered angles are adjacent or nonadjacent. 2 a. 1 a. Because the angles do not share a common vertex or a common side, then ∠1 and ∠2 are nonadjacent.
- 17. • Tell whether the numbered angles are adjacent or nonadjacent. b. 3 4 Because the angles share a common vertex and a common side, and they do not have an common interior points,∠3 ∠ and 4 are adjacent.
- 18. • Tell whether the numbered angles are adjacent or nonadjacent. c. 5 6 Although ∠5 and ∠6 share a common vertex, they do not share a common side. Therefore, ∠5 ∠6 and are nonadjacent.
- 19. Example Measures of Complements and Supplements a. ∠A is a complement of ∠C, and m∠A = 47°. Find m∠C. b. ∠P is a supplement of ∠R, and m∠R = 36°. Find m∠P. SOLUTION a. ∠A and ∠C are b. ∠P and ∠R are supplements, complements, so their so their sum is 180°. sum is 90°. 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°
- 20. Checkpoint Measures of Complements and Supplements 4. ∠B is a complement of ∠D, and m∠D = 79°. Find m∠B. ANSWER 11° 5. ∠G is a supplement of ∠H, and m∠G = 115°. Find m∠H. ANSWER 65°
- 21. Congruent Complements Theorem 2 3 1 1
- 22. Congruent Supplements Theorem 2 3 1 1
- 23. ∠7 and ∠8 are supplementary, and ∠8 and ∠9 are supplementary. Name a pair of congruent angles. Explain your reasoning. SOLUTION ∠7 and ∠9 are both supplementary to ∠8. So, by the Congruent supplements Theorem, ∠7 ≅ ∠9.
- 24. In the diagram, m∠10 + m∠11 = 90°, and m∠11 + m∠12 = 90°. Name a pair of congruent angles. Explain your reasoning. ∠10 ≅ ∠12; ∠10 and ∠12 are both ANSWER complementary to ∠11, so ∠10 ≅ ∠12 by the Congruent Complements Theorem.
- 25. More drawings F E 20 90 70 D G C 70 90 J 20 I H
- 26. Final Drawing B C 68 52 60 A G D 60 52 68 F E