The AC side of the triangular ABC passes through the center of the circumscribed circle around it.

The AC side of the triangular ABC passes through the center of the circumscribed circle around it. Find angle C if angle A is 75 degrees.

Triangle ABC is inscribed in a circle, then all its vertices lie on the circle. The AC side is the diameter of the circumscribed circle, since it passes through the center of this circle. Then the angle B = 90 degrees, since the inscribed angle based on the diameter is right. By the theorem on the sum of the angles of a triangle:
angle A + angle B + angle C = 180 degrees;
75 + 90 + angle C = 180;
angle C = 180 – 165;
angle C = 15 degrees.
Answer: angle C = 15 degrees.