An isosceles triangle has its base extended, forming an exterior angle of 130°. The two base angles are equal. Find each base angle.

Extending the base at one base vertex: the exterior angle and the base angle form a linear pair, so base angle = 180 - 130 = 50°. Check: the two base angles are equal (50 each), apex = 180 - 2(50) = 80, and exterior at base vertex = apex + other base = 80 + 50 = 130. Consistent. Each base angle = 50°.