The AC side of triangle ABC passes through the center of the circle. Find ∠C if ∠A = 83 °.

bystudin | May 31, 2020 | Education

Because AC is a diameter, so the triangle ABC is right-angled with the hypotenuse AC and ∠B = 90 ° (by the circumscribed circle theorem).
Then, by the theorem, the sum of the angles of a triangle:
180 ° = ∠A + ∠B + ∠C
180 ° = 83 ° + 90 ° + ∠C
∠C = 180 ° -83 ° -90 °
∠C = 7 °
Answer: ∠C = 7 °

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