The measure of an interior angle of a regular polygon is 135 degrees. Find the number of sides in the polygon. This is what I tried:

180(x-2)=135 [Interior Angle Sum Theorem]
x-2=.75
x=2.75

That can't be right though. Help?

Not sure about your formula.

Number of sides = 360/(180-interior angle)

so

Number of sides = 360/(180-135)
= 360/45
= 8

180(x-2) gives you the SUM of the interior angles, so each angle would be 180(x-2)/x

your equation would be

180(x-2)/x = 135

Sove it, you will get the answer DrRuss got.

4 answers

180°-360°/n=108°

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