Question

In the figure below, AC = BC and ∠C = 40°. What is the measure of ∠A? *50°60°65°70°75°

Answer 1

It's important to know that the given triangle ABC is isosceles because it has two equal sides AC = BC. Isosceles triangles have equal base angles, which means angles A and B are equal.

Using the interior angles theorem, we have

`\begin{gathered} m\angle A+m\angle B+m\angle C=180 \\ m\angle A+m\angle A+40=180 \\ 2\cdot m\angle A=180-40 \\ m\angle A=(140)/(2) \\ m\angle A=70 \end{gathered}`

Therefore, angle A measures 70°.