Question 1162499
<pre>
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:

{{{drawing(400,5400/17,-2.4,1,-.5,2.2,

line(-2,0,0,0), line(0,0,1/2,sqrt(3)/2), line(1/2,sqrt(3)/2,0,sqrt(3)),
line(0,sqrt(3),-1,sqrt(3)), line(-1,sqrt(3),-2,0),
locate(-1,1.74,120^o),
locate(-.26,.27,120^o),
locate(-.26,1.74,120^o),
locate(-1.9,.21,60^o),
locate(.15,1,120^o),
locate(-2,0,A), locate(0,0,B), locate(.51,.95,C),
locate(0,1.9,D), locate(-1.03,1.9,E) 



)}}}

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</pre>