Question

Let $ABCDE$ be an equilateral pentagon. If the pentagon is concave, and $\angle A = \angle B = 120^{\circ},$ then what is the degree measure of $\angle E$?

Answer 1

60°

Explanation:

You want the measure of angle E in equilateral pentagon ABCDE with angles A and B both 120°.

Figure

A drawing of the pentagon is attached. Given that anlges A and B are 120°, segments CD and DE must form a straight line.

The angle at E will be 60°.

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Additional comment

Triangles ADE, ABD, and BCD are congruent equilateral triangles.

The sum of all interior angles is 540°. Angles A and B total 240°. The angle at D is 180°, so the sum of congruent angles C and E will be 120°. Each must be 60°, consistent with those being the interior angles of an equilateral triangle.

The pentagon is not concave. There is no reflex interior angle.

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