1. Angle Relationships in circles

2. If a tangent and a chord intersect, then the measure of the angle is ½ the arc.
113 * 2 = 226
90 * 2 = 180
164/2 = 82

3. If 2 chords intersect, then each angle is ½ the sum of the arc and its vertical angle.
To find x:
To find y:
= 142
= 218
142/2 = 71
218/2 = 109

4. If tangents and secants intersect outside the circle, then the angle is ½ the difference of the arcs.
175 – 35 = 140
115 – 25 = 90
140/2 = 70
90/2 = 45

5. A little more challenging
First find arc 1
= 304
= 78
360 – 304 = 56
78/2 = 39
arc 1 = 56