Mark the angles a, x and y. Then find the other angles, because we have right angle triangles. Also we have identical triangles, as the sides are tangents from A , B C and D on to the circle. So the lengths of tangent segments on to the circle are equal. Thus the angles inside the two adjacent triangles are equal.
Sum of all angles at the center = 360 deg
135-a + 135-a + a + a + 2 x + 2 y = 360 deg
2x + 2y = 90 deg
x + y = 45 deg = angle BOC.