SOLUTION: 135� is the measure of the interior angle, what is the value of "n" in n-gon?

Question 1012347: 135� is the measure of the
interior angle, what is the value of "n" in n-gon?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!
.
135� is the measure of the
interior angle, what is the value of "n" in n-gon?
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The sum of interior angles of an n-sided polygon is 180*(n-2)
(see the lesson Sum of interior angles of a polygon in this site).

It gives you an equation

n*135 = 180*(n-2).

Simplify and solve it:

3n = 4*(n-2),

3n = 4n - 8,
'
n = 8.

Answer. n = 8.

Answer by MathTherapy(10551) (Show Source): You can put this solution on YOUR website!

135� is the measure of the
interior angle, what is the value of "n" in n-gon?

This appears to be a REGULAR n-gon.
Since one of its interior angles is , it follows that one of its exterior angles = ()
With an exterior angle being , number of sides, or n = , or .
FYI: This is an OCTAGON.
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