Question 1210529
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The described figure does not exist.<br>
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.<br>
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+x/sqrt(2)}}}; the length of that hypotenuse is {{{sqrt(2)(x+x/sqrt(2))=x(1+sqrt(2))}}}, which is greater than 2x.<br>
The problem is faulty; or else the "answer" to the problem is that there is no such figure.<br>