In an isosceles triangular ABC with base AB, the outer angle at the apex B is 130 degrees. Find the angle C.

An isosceles triangle is a triangle whose base angles are equal.

In this case, angle A is equal to angle B, since AB is the base.

It is known that the sum of the inner and adjacent outer angles of a triangle is 180 °.

It follows that the angle B = A = 180 – 130 = 50 °.

So angles A and B are 50 °.

The angles of any triangle add up to 180 °. Hence the angle C is:

C = 180 – A – B = 180 – 50 – 50 = 80 °.

Answer: C = 80 °.