SOLUTION: Let ABCDE be an equilateral pentagon. If the pentagon is concave, and angle A = angle B = 135, then what is the degree measure of angle E?

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Question 1210529: Let ABCDE be an equilateral pentagon. If the pentagon is concave, and angle A = angle B = 135, then what is the degree measure of angle E?
Answer by greenestamps(13295) About Me  (Show Source):
You can put this solution on YOUR website!


The described figure does not exist.

If each side of the pentagon has length x and the measures of angles A and B are each 135 degrees, then the distance from C to E is greater than 2x, making it impossible for the pentagon to be equilateral.

With the given conditions, again letting x be the length of each side of the equilateral pentagon, extend sides CB and EA to meet at F. Then the distance from C to E is the hypotenuse of isosceles right triangle EFC with side length x%2Bx%2Fsqrt%282%29; the length of that hypotenuse is sqrt%282%29%28x%2Bx%2Fsqrt%282%29%29=x%281%2Bsqrt%282%29%29, which is greater than 2x.

The problem is faulty; or else the "answer" to the problem is that there is no such figure.