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.
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