An isosceles triangle ABC with the base BC is inscribed into a circle. Find the measure of angles of it, if measure of arc BC=102°.

Answer 1

First, draw a diagram.

Since ΔABC is isosceles, sides AB and AC are congruent. AB and AC are chords of the circle, so arc AB is congruent to arc AC.

arc AB + arc AC + 102° = 360° So, arc AB = arc AC = 129°

angles A, B, and C are inscribed angles.

So, ∠A = (1/2)(arc BC) = 51˜

∠B = (1/2)(arc AC) = 64.5°

∠C = (1/2)(arc AB) = 64.5°