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Answers 10.4 Practice A 1. 20 2. 144 3. 58 4. B; Sample answer: RQS and RPS are inscribed angles that intercept the same arc, so the angles are congruent by the Inscribed Angles of a Circle Theorem (Thm. 10.11). 5. x 110, y 67 6. x 99, y 90 7. x 39, y 29 8. Opposite angles should be supplementary, not congruent; mB 95 with hypotenuse AB. So, AB is a diameter of the circle by the Inscribed Right Triangle Theorem (Thm. 10.12). 10.5 Practice A 1. 202 2. 102 3. 56 5. 42 6. 35 7. 26 4. 133 8. Sample answer: This finds the supplement of the angle labeled x. The measure of the angle should be one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle; 1 mx 66 66, so mx 66. 2 9. a. 62.3 9. 21 b. 83.1 c. acute, scalene; Sample answer: Because mA 34.6, mB 62.3, and mC 83.1, ! ABC has three acute angles and no congruent sides. 1. 60 2. 30 3. 60 4. 60 5. 30 6. 60 7. D; The measure of 4 is one-half the sum of the 10.4 Practice B 1. 90 2. 42 3. 58 4. 48 5. 58 6. 42 7. 96 8. 180 9. x 14, y 38 10.5 Practice B 10. x 72, y 90 measures of the arcs intercepted by the angle and its vertical angle. So, 1 m4 75 125 100 90. 2 8. 50 11. x 16, y 14 9. 7 10. 70 11. a. 120 12. Sample answer: STATEMENTS 1. P 2. AED BEC 3. CAD DBC 4. ! AED ! BES b. 100 REASONS c. 140 1. Given 12. about 6.8 2. Vertical Angles Congruence Theorem (Thm. 2.6) 10.6 Practice A 3. Inscribed Angles of a Circle Theorem (Thm. 10.11). 4. AAA Similarity Theorem (Thm. 8.3) 13. yes; Sample answer: ADB and BCA intercept the same arc, so the angles are congruent by the Inscribed Angles of a Circle Theorem (Thm. 10.11). 14. yes; Sample answer: mCAB 60 by the 1. 15 2. 2 3. 12 4. 5 5. 6 6. 7 7. 15 8. 12 9. 4 10. 4 11. 4 12. 7 13. about 14.2 ft 10.6 Practice B 1. 10 2. 8 3. 4 4. 4 5. 8 6. 15 7. 9 8. 5 9. 30 10. about 20.1 in. 11. about 139.8 in. Measure of an Inscribed Angle Theorem (Thm. 10.10) and mACB 90 by the Triangle Sum Theorem (Thm. 5.1). ! ABC is a right triangle Copyright © Big Ideas Learning, LLC All rights reserved. Geometry Answers A1 Answers 10.7 Practice A 6. x 4 y 1 25 7. x 2 y 4 169 1. x 2 y 2 49 x 2. 5 y 1 25 2 2 2 2 2 2 8. center: 0, 0, radius: 10 3. x 2 y 2 64 4. x 2 y 5 2 4 5. x 2 y 2 25 x 6. 3 y 2 841 2 2 7. B 8. A 9. C 10. center: 0, 3, radius: 2 11. Sample answer: The distance from point 3, 3 to the origin is 3 2, but the radius of the circle is 4, so the point does not lie on the circle. 12. a. from left to right, top row: x x x 28 y 44 169, 2 2 57 y 44 169, 2 2 86 y 44 169; 2 2 from left to right, bottom row: x x 42.5 y 31 169, 2 2 71.5 y 31 169 2 2 b. Sample answer: Subtract 3 from the radius to obtain 100 on the right side of each equation. 10.7 Practice B 1. x 2 y 2 9 2. x 3 y 2 4 3. x 4 y 7 16 4. x 3 y 2 25 2 2 2 2 2 5. x 2 y 2 1 A2 Geometry Answers Copyright © Big Ideas Learning, LLC All rights reserved. Answers 9. center: 2, 9, radius: 2 10. center: 0, 2, radius: 6 11. center: 1, 0, radius: 2 12. Sample answer: The statement is true. The distance from point 3, 4 to the origin is 5, and the radius of the circle is 5, so the point lies on the circle. 13. Sample answer: The statement is false. The distance from point 2, 3 to the origin is 7, but the radius of the circle is 3, so the point does not lie on the circle. 14. a. b. 2, 4 c. no; The point 4, 5 is about 10.8 miles away from the epicenter. Copyright © Big Ideas Learning, LLC All rights reserved. Geometry Answers A3