Find the value of x. (picture tagged)

Question

kymber · Answer

Where's the peeeeeeeeeeeeeeeeeeekcha

anonymous · Answer

|dw:1332966459714:dw|

anonymous · Answer

thats supposed to be a X lol

anonymous · Answer

Well it seems like the first thing to do is get the measurement of the 5 outside segments.  

2pi/5.

anonymous · Answer

1.256?

anonymous · Answer

@kymber do you remember this stuff?

anonymous · Answer

its multiple choice if that helps?
a) 36
b) 72
c) 108
d) 216

anonymous · Answer

Okay the total degrees inside a pentagon are 540 degrees.  From the picture, you have 5 equal sides.  Therefore, the angle of each corner of the pentagon is 108 degrees.  That also means the opposite angle is 108 degrees.  

Therefore x degrees = 108 degrees

Sorry I kept stumbling on this problem, it's been 10 years since I've had to do this sort of thing.

anonymous · Answer

thanks(:

anonymous · Answer

Can you see how since the 5 segments of the circle are equal, that the 5 sides of the pentagon also have to be equal?  

And since that is true, all 5 angles inside the pentagon are also equal?