# An isosceles triangle ABC with base BC is inscribed in a circle. Find the angles of a triangle

September 28, 2021 | education

| **An isosceles triangle ABC with base BC is inscribed in a circle. Find the angles of a triangle if the arc is BC = 102 degrees**

Given: ΔABC – isosceles inscribed in a circle.

AB = AC.

BC = 102 °.

∠A -? ∠B -? ∠C -?

Solution:

Let us find the angle at the vertex of an isosceles triangle as half the degree measure of the arc:

∠A = 1/2 * 102 ° = 51 °.

Find two equal angles at the base of an isosceles triangle.

∠В = ∠С = 1/2 (180 ° – 51 °) = 129/2 = 64 ° 30 ‘.

Answer: 51 °; 64 ° 30 ‘; 64 ° 30 ‘.

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