Angle A = 50 degrees, angle C = 130 degrees, sides AB and CB are equal, find unknown angles.

The condition says that the angle A is 50 °, the outer angle at the vertex C is 130 °, and it is also known that AB = CB.

In order to find unknown angles, let’s remember the properties of the outer corner of a triangle. The outer angle of a triangle is equal to the sum of two angles of the triangle that are not adjacent to it.

In other words, the outer angle C is equal to the sum of the inner angles A and B.

130 ° = 50 ° + B;

Angle B = 80 °.

And since the sides of the triangles are AB = CB, the triangle is equilateral and the angles at the base are equal to each other:

Angle A = angle C = 50 °.