Each base angle is 80° and vertex angle is 20°.
The triangle is shown for the given scenario.
From the isosceles triangle ABC, sides AB and AC are equal. So, angle B is equal to angle C.
Let the base angles be equal to .
Therefore, the exterior angle of the base and the base angle form a linear pair and thus are supplementary angles.
For two angles to be supplementary, their sum is 180 degrees.
So, each of the base angle is 80°.
Now, for a triangle ABC, the exterior angle is equal to the sum of the opposite interior angles. Therefore,
Therefore, the angle at the vertex is 20°.