Find the measure of angle a formed by the tangent lines. (see image)

Question

https://i.imgur.com/b2BN2Pt.png

(A) 75º

(B) 150º

(C) 105º

(D) 115º

(E) none of these

Answer 1

1. Draw a radius from the center of the circle to each point of tangency. These radii form a right (90°) angle with each tangent line.
2. The central angle formed by the center and two radii in step 1 subtends the 75 degree arc, so it is also 75 degrees.
3. The tangent lines and the radii you drew form a quadrilateral. You know three of the angles within that quadrilateral: 90°, 90°, and 75°. The missing angle is the one between the tangent lines. The sum of the angles within a quadrilateral is 360°. Can you finish it from here?