SOLUTION: Four angles of a pentagon are equal and the fifth is 60°. Find the equal angles and show that two sides of the pentagon are parallel.

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Question 1162499: Four angles of a pentagon are equal and the fifth is 60°. Find the equal angles and show that two sides of the pentagon are parallel.
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


What don't you understand about this and what have you tried so far?


John

My calculator said it, I believe it, that settles it
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
The sum of the interior angles of a pentagon have sum

(n-2)∙180° = (5-2)∙180° = 3∙180° = 540°.
One of the interior angles is 60°
So the other 4 interior angles have sum 540°-60° = 480°
Since the other 4 angles are equal, they measure 480°÷4 = 120° each.
The figure looks like this:



AB ∥ ED because m∠A + m∠E = 60° + 120° = 180° 
(if angles on the same side of two lines AB, ED, are supplementary when AB
and ED are cut by the transversal AE, then the two lines are parallel. 

AE ∥ BC because m∠A + m∠B = 60° + 120° = 180° 
(if angles on the same side of two lines AE, BC are supplementary when AE
and BC are cut by the transversal AB, then the two lines are parallel.

Edwin
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