The arc measure is some unknown number x, so is the angle formed by the tangents that form based on this arc. The arc and angle add to 180, so,
x+x = 180
2x = 180
2x/2 = 180/2
x = 90
A right angle forms if we were to draw segments from the center of the circle to the points of tangency. We have a square forming if we do so. Recall that the points of tangency have the radius and tangent segments meet up at a 90 degree angle.
