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10.5 – Apply Other Angle Relationships in Circles

10.5 – Apply Other Angle Relationships in Circles . tangent. chord. If a __________ and a ________ intersect at a point _____ a circle, then the measure of each angle formed is _______ the measure of its intercepted arc. on. half. Arc 2. Tangent angle =. chords. inside.

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10.5 – Apply Other Angle Relationships in Circles

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  1. 10.5 – Apply Other Angle Relationships in Circles

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

  3. chords inside 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. half sum vertical (arc + arc) 2 Inside angle =

  4. tangent chord 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. outside half difference big arc – little arc 2 Outside angle =

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

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

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

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

  9. Find the measure of each indicated angle or arc. big arc – little arc 2 Outside angle = 56° 134 – 56 2 m2 = 78 2 m2 = m2 = 39° 360 – 170 – 134 56°

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

  11. Find the measure of each indicated angle or arc. arc + arc 2 Inside angle = x + 66 2 74° 70 = 1 x + 66 = 140 x = 74° 360 – 66 – 126 – 74 Arc 2 = 94° Arc2 =

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

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

  14. Find the measure of each indicated angle or arc. big arc – little arc 2 Outside angle = 222° 222 – 138 2 m1 = 84 2 m1 = m1 = 42° 360 – 138 222°

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

  16. HW Problem 10.5 #10 big arc – little arc 2 Outside angle = 247 – 113 2 113° x = 134 2 x = 360 – 247 x = 67° 113°

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