10.5 – Apply Other Angle Relationships in Circles
Dec 29, 2015
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