Interview Question for Software Engineer at SolidWorks:

We can split the triangle in two by drawing a line from the centre of the circle to the point on the circumference our triangle touches. We know that each of the lines which is a radius of the circle (the green lines) are the same length. Therefore each of the two triangles is isosceles and has a pair of equal angles. But all of these angles together must add up to 180°, since they are the angles of the original big triangle. Therefore x + y + x + y = 180, in other words 2(x + y) = 180. And so x + y = 90. But x + y is the size of the angle we wanted to find.