1. 10.5 – Apply Other Angle Relationships in Circles

2. If a __________ and a ________ intersect at a point _____ a circle, then the measure of each angle formed is _______ the measure of its intercepted arc. tangentchord on half Tangent angle = Arc 2

3. If two _________ intersect ____________ a circle, then the measure of each angle is __________ the _____ of the measures of the arcs intercepted by the angle and its ____________ angle. chordsinside halfsum vertical Inside angle = (arc + arc) 2

4. If a __________ and a ____________, two tangents, or two secants intersect ___________ of a circle, then the measures formed is ________ the ______________ of the measures of the intercepted arcs. tangentchord outside halfdifference Outside angle = big arc – little arc 2

5. Find the measure of each indicated angle or arc. Tangent angle = Arc 2 234° 126° 117 = x2x2 1 x = 234° 360 – 234°

6. Find the measure of each indicated angle or arc. m  2 = 115+97 2 m  2 = 212 2 m  2 = 106° m  1 = 180 – 106 m  1 = 74° Inside angle = arc + arc 2 106°

7. Find the measure of each indicated angle or arc. m  1 = 92 – 43 2 m  1 = 49 2 m  1 = 24.5° Outside angle = big arc – little arc 2

8. Tangent angle = Arc 2 3x – 1 =5x + 33 2 1 5x + 33 = 2(3x – 1) 5x + 33 = 6x – 2 33 = x – 2 35° = x Find the measure of each indicated angle or arc.

9. m  2 = 134 – 56 2 m  2 = 78 2 m  2 = 39° 360 – 170 – 134 56° Outside angle = big arc – little arc 2

10. m  1 = 243 – 117 2 m  1 = 126 2 m  1 = 63° Find the measure of each indicated angle or arc. 360 – 243 117° Outside angle = big arc – little arc 2

11. 70 = x + 66 2 x + 66 = 140 x = 74° Arc 2 = 360 – 66 – 126 – 74 Arc 2 = 94° Inside angle = arc + arc 2 1 Find the measure of each indicated angle or arc. 74°

12. Tangent angle = Arc 2 84° 84 = x2x2 1 x = 168° Find the measure of each indicated angle or arc. 180 – 96 84°

13. 38 = x + 10x – 1 2 11x – 1 = 76 11x = 77 Inside angle = arc + arc 2 1 x = 7° Find the measure of each indicated angle or arc.

14. m  1 = 222 – 138 2 m  1 = 84 2 m  1 = 42° 360 – 138 222° Outside angle = big arc – little arc 2

15. Find the measure of each indicated angle or arc. 61 = (10x + 1) – (5x – 1) 2 1 (10x + 1) – (5x – 1) = 122 10x + 1 – 5x + 1 = 122 5x + 2 = 122 5x = 120 x = 24 Outside angle = big arc – little arc 2

16. 10.5 Review 683-685 914-915 3-5, 7, 10-12 15-17, 31, 32, 34, 37-41 HW Problem 10.5 #10 x = 247 – 113 2 x = 134 2 x = 67° 360 – 247 113° Outside angle = big arc – little arc 2