Question

A triangle ABC is inscribed in a circle, such that AB is a diameter. What are the measures of angles of this triangle if measure of arc BC = 134°

Answer 1

∠C=90°

∠A=67°

∠B=23°

Explanation:

For angle C:

Thales' Theorem states that an angle inscribed across a circle's diameter is always a right angle.

Therefore, since AB is the diameter(hypotenuse) then angle C is the right angle. (90°)

For Angle A:

The measure of arc BC= 134 degrees. We can just use a formula for an inscribed triangle. ∠A = 1/2 (mBC)

∠A= (1/2)134

∠A= 77°

For angle B:

All triangle angles all add up to 180. We can just subtract angles A and C from 180°:

∠B = 180-(90+67)

∠B = 23°