Find the angles of an isosceles triangle inscribed in a circle, the side of which contracts an arc of 50 degrees.

Since the lateral side contracts the arc by 50 °, the angle opposite to this side is measured in half of this arc, that is, it is equal to 25 ° (inscribed angle). By the condition, the triangle is isosceles, and the found angle is the angle at the base, from this we get that the second angle is also 25 °.

The sum of the angles in the triangle is 180 °, therefore the third angle is 180 ° – (25 ° + 25 °) = 130 °.

In the end, we get: two angles are equal to 25 °, the third angle is 130 °.