10.5 – Apply Other Angle Relationships in Circles

If a __________ and a ________ intersect at a point _____ a circle, then the measure of each angle formed is _______ the measure of its intercepted arc.

tangent chordon

half

Tangent angle = Arc 2

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.

chords inside

half sum

vertical

Inside angle = (arc + arc) 2

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.

tangent chordoutside

half difference

Outside angle = big arc – little arc 2

Find the measure of each indicated angle or arc.

Tangent angle = Arc 2

234°

126°

117 = x21

x = 234°

360 – 234°

Find the measure of each indicated angle or arc.

m2 = 115+97 2

m2 = 212 2

m2 = 106°

m1 = 180 – 106

m1 = 74°

Inside angle = arc + arc 2

106°

Find the measure of each indicated angle or arc.

m1 = 92 – 43 2

m1 = 49 2

m1 = 24.5°

Outside angle = big arc – little arc 2

Tangent angle = Arc 2

3x – 1 = 5x + 33 21

5x + 33 = 2(3x – 1)

5x + 33 = 6x – 2

33 = x – 2

35° = x

Find the measure of each indicated angle or arc.

Find the measure of each indicated angle or arc.

m2 = 134 – 56 2

m2 = 78 2

m2 = 39°360 – 170 – 134

56°

56°

Outside angle = big arc – little arc 2

m1 = 243 – 117 2

m1 = 126 2

m1 = 63°

Find the measure of each indicated angle or arc.

360 – 243

117°

117°

Outside angle = big arc – little arc 2

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°

Tangent angle = Arc 2

84°84 = x

21

x = 168°

Find the measure of each indicated angle or arc.

180 – 96

84°

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.

Find the measure of each indicated angle or arc.

m1 = 222 – 138 2

m1 = 84 2

m1 = 42°360 – 138

222°

222°

Outside angle = big arc – little arc 2

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

10.5Review

683-685914-915

3-5, 7, 10-1215-17, 31, 32, 34, 37-41

HW Problem

10.5 #10

x = 247 – 113 2

x = 134 2

x = 67°360 – 247

113°

113°

Outside angle = big arc – little arc 2