Side AC of triangle ABC passes through the center of the circle circumscribed about it.

Side AC of triangle ABC passes through the center of the circle circumscribed about it. Find angle C if angle A = 53 degrees

The AC side passes through the center of the circumscribed circle around it, which means that the diameter of the circle is equal to AC. If the diameter of the circle is equal to the side of the inscribed triangle, then this triangle is rectangular (with an angle = 90 °), and this side of the triangle is its hypotenuse.

The sum of all angles in any triangle is always 180 °. So the sum of the acute angles at the hypotenuse of a right triangle is 90 °. So the angle C is equal to:

∠ С = 90 ° – ∠ А = 90 ° – 53 ° = 37 °.

Answer: 37 °