**Let the third time be the CHARM:**

Let Y be the point on the circle where segment PY and segment XY intersect

Let Z be the point on the circle where segment PZ and segment XZ intersect

measure of angle PYX = 90° and measure of angle PZX = 90° because:

**RADIUS OF A CIRCLE IS PERPENDICULAR TO A LINE DRAWN TANGENT **

**TO THE** **CIRCLE AT THE POINT OF TANGENCY**

(in your drawing points Y and Z are the points of tangency)

Given: arc YZ = 100° from the drawing

measure of angle YPZ = 100° because a **CENTRAL ANGLE IS EQUAL **

**IN MEASURE TO THE ****ARC IT CUTS OUT**

Looking at quadrilateral XYPZ, the sum of its interior angles is 360°

angle Y = 90°, angle P = 100°, angle Z = 90°; **360 -280 = 80**

**Therefor the measure of angle X = 80°**

I worked this problem using Polygons and the sum of their interior angles.

It can also be worked using congruent triangles.

Let me know if you want to see the triangular method.

Kelly T.

08/18/16