assume that the lines that appear to be tangent are tangent. P is the center of the circle. What is the value of x?

Question

Answer 1

The measure of an angle formed by two tangents = 1/2 the difference of the measure of the intercepted arcs.

Let the arc nearest the 72 degree angle be y, then the outer arc is 360 - y, so

72 = 1/2 (360 - y- y)

144 = 360 - 2y

-216 = 2y

y = 108

y = 108 is also the measure of the arc intercepted by the central angle x.

The measure of a central angle is equal to the measure of intercepted arc, so x = 108.