Question

An isosceles triangle △ABC with the base BC is inscribed in a circle. Find the measures of angles of the triangle, if measure of arc BC is 102°.

Answer 1

• angle at A: 51°
• base angles: 64.5°

Explanation:

The measure of the inscribed angle BAC is half the measure of the intercepted arc BC, so is 102°/2 = 51°.

The base angles at B and C are the complement of half this value, or ...

90° -(51°/2) = 64.5°

The angle measures in the triangle are ...

∠A = 51°

∠B = ∠C = 64.5°