Angle Relationships in circles

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

If 2 chords intersect, then each angle is ½ the sum of the arc and its vertical angle. To find x: To find y: 85 + 57 = 142 148 + 70 = 218 142/2 = 71 218/2 = 109

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

A little more challenging First find arc 1 170 + 134 = 304 134 - 56 = 78 360 – 304 = 56 78/2 = 39 arc 1 = 56