An isosceles triangle has a vertex angle of 40°, formed by its two equal sides. What is the measure of each base angle?

In an isosceles triangle, the angles opposite the equal sides are equal. The vertex angle of $40°$ is between the two equal sides, so the other two angles are the base angles and they are equal. The angles of a triangle sum to $180°$, so the base angles together measure $180° - 40° = 140°$. Each base angle is $\frac{140°}{2} = 70°$, choice C. Check: $70 + 70 + 40 = 180$. Choice A (40°) assumes all angles are equal. Choice B (140°) is the combined measure of both base angles. Choice D (80°) would make the angle sum $200°$.