Circles have 360 degrees. Triangles have 180 degrees. When you see a simple 2 to 1 ratio you know something's up. Here the vertices of our triangle are forced to stay on the circle. Pick a vertice and move it. Notice how it changes or doesn't change.

The angle of an arc as measured from the center of a circle is always twice the angle measured from any point on the circle. Here we divide the circle into three arcs with our triangle, and in every case, the 360 degrees of the circle relate to the 180 degrees of the triangle.