The angle is 60 degrees.
Work Step by Step
First, draw the circle, placing point Q at the center. Then, recall that the tangent to the circle is the line that is parallel to the circle when it goes through the edge of the circle. Thus, drawing point V, draw the tangent segments, starting at point V. Be sure to put V in a spot that makes the lengths of the segments equal to the diameter. Once this is drawn, you will have an equilateral triangles, where all angles are 60 degrees. Thus, the measure of the desired angle is 60 degrees.