Question

Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.)

Answer 1

x = 64.

Explanation:

If PQ is a segment on a tangent to the circle at point Q (as per the question), then <OQP is a right angle, so m<OQP=90 degrees. The angles in the triangle OPQ will need to sum up to 180 degrees. We are given m<OPQ=26 degrees. It remains to be determined the angle x = 180 - 90 - 26 = 64.