University:
Missouri State University
Course:
MTH 460 | College Geometry
Academic year:

2019
Views:

174

Pages:

2
Author:

Prince Sampson

NAME Answer Key Inscribed Angles In Exercises 1-6 find the values of a, b, and c. In Exercises 1, 3, and 6, O is the center of the circle. DATE SCORE For use after Section 9-5 1. 110 40° 2. b 110 105° 95 3. 85 a = 75/80 4. 112 82° 0 62 124 b 56 5. 110" 100% 80° 6. 70 6-100 A 20.0 100% a= 90^ b= 105/(10 deg) Supply the missing statements and reasons. 7. Given: m overline ZW =m hat XY 1. n7. w = mxy Prove: m angle ZYX =m angle YZW Proof: Statements 2. m overline ZW +m overline WX =m overline WX +m overline XY 3. m hat ZW +m hat WX =m hat ZX ; m overline WX +m hat XY =m hat WY 4. mwy 5. 1/2 m overline ZX = 1 2 m overline WY 6. mLZYX=mZX; n angle YZW = 1 2 m hat WY 7. mLZYX = MLYZW W X Y Reasons Skip Addition Property 1. Given 2. 3. Arc Addition Postulate 4. Substitution Property 5. Multiplication the measure of an inscribed angle 6. is dual to half the intercepted are. 7. Substitution 52 a = (90 deg)/(b = 41/(98 deg)) a= 5b b= 62 124 a = 50 deg b = (100 deg)/(c = 40 deg) a = 30/(b = 20) c = 15 deg NAME Other Angles In Exercises 1-4 overline AB * and - CD are chords. 1. If and m overline DB = mathbb A 3, then 2. If m hat AD = 136 ; and m overline CB = 96 , then DATE SCORE For use after Section 9- A D 1 Skip 3. If and mAC 78, then m overline DB 4. If and m hat DB = 42 , then mA overline C = B C Exs. 1-4 In Exercises 5-7 overline EF and overline EG are tangents. F 5. If m overline FHG = 280 , then 6. If m hat FG = 96 , then m angle E = 100/84 E 7. If m angle E = 90 , then m overline FHG = 270 G Exs. 5-7 90 = 1/2 * (x - (360 - x)) 1/2 * (280 - 80) 7 * 1/2 * (264 - 96) In Exercises 8-10 overline D is a tangent. 8. If m. overline IK = 120 and then 1/2 * (120 - 40) m overline \mathcal{L} = 40 , m angle I= 40 1.1 * 0.6 . L K 9. If m angle I = 45 and then 45 / (1/2) * (x - 55) m hat JL = 55 , m J hat K =\ 145 10. If m angle I = 50 and then 50 = j/2 * (110 - x) m overline JK = 110 , m overline JL = 10 J . 8-10 80 In Exercises 11-15 overline RP and overline RT are secants. P 1/2 * (100 - 20) 11. If and m hat QS = 20 , then 12. If m hat PT = 130 and m overline QS = 40 , then m angle R= 40 m angle R = 45/7 . m hat PT = 100 Q 1/2 * (136 - 40) R 1130 S 25 = 1/2 * (x - 25) 13. If m angle R = 25 and m overline QS = 25 , then m hat pT = 15/(6r) 90 T 4t = 1/2 * (130 - x) 14. If and mPT 130, then m hat Qs = 50 15. If m overline ST = 90 , m overline QS = 60 , and m hat QP = 80 , then m angle R = 35 Exs. 11-15 1/2 * (130 - 60) In Exercises 16-19 tangent to the circle at point E. 16. If m hat AG = 100 and m hat BH = 20 , then 17. If m angle C = 25 and m overline BH = 25 , then m angle C= 40 m overline AG = 75 A B C H 18. If and m overline G overline E = 25 , then m angle D = 3b 19. If m angle D = 40 and m overline EH = 138 , then m hat GE = 58 25 = 1/2 * (x - 25) 40 = 1/2 * (138 - x) 1/2 * (10 - 20) 1/2 * (95 - 25) G D B Exs. 16-19