The isosceles triangle ABC with the base BC is inscribed in the circle. find the angles of the triangle

The isosceles triangle ABC with the base BC is inscribed in the circle. find the angles of the triangle if the BC arc is -102 degrees.

Angle A of triangle ABC rests on arc BC.

Angle A is inscribed in a circle. The inscribed angle is equal to half of the arc on which it rests.

Hence, the angle A is 102 ° / 2 = 51 °.

In an isosceles triangle, the angles at the base are equal. If the base of the triangle is BC, then the angle B is equal to the angle C.

The angles of a triangle add up to 180 °. So the sum of the angles B and C is equal to:

180 ° – 51 ° = 129 °.

B = C = 129 ° / 2 = 64.5 °.