SOLUTION: How many sides does a regular polygon with each interior angle equal to 135 degrees?

Algebra ->  Polygons -> SOLUTION: How many sides does a regular polygon with each interior angle equal to 135 degrees?       Log On


   

Question 378611: How many sides does a regular polygon with each interior angle equal to 135 degrees?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Note that the formula for the number of degrees of an n-sided convex polygon is 180%28n-2%29. If the polygon is regular, the interior measure of each angle is %28180%28n-2%29%29%2Fn.
If each interior angle is 135 degrees, then we can plug 135 for the interior measure and solve for n:
135+=+%28180%28n-2%29%29%2Fn
135n+=+180n+-+360
n+=+8
Thus, a regular octagon has interior angle measure of 135 degrees.