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The sum of the interior angles of a polygon is (n-2)*180 where n is the number of sides (and angles).
Is this a triangle (three angles)? 90 + 135 + 135 - NO!
It can't be a square, because all the angles have to be right.
This is taking too long, let's find a formula. The interior angles of an n sided (thus n angled) polygon must equal (n-2)180. That same n sided polygon, in this example, has one 90 degree angle and (n-1) 135 degree angles. That's because one of the n angles is 90, leaving n-1 angels at 135. So that gives us a formula:
(n-2)*180 = 90 + (n-1)*135 Multiple the numbers by what's in the ().
180n - 360 = 90 +135n -135 Subtract 135n from both sides, add 360.
45n = 315 divide both sides by 45.
n = 7 ---> This is a 7-sided polygon, thus it has 7 interior angles, with one 90 degrees and the others 135. Let's check it.
(7-2)*180 = 90 + 6(135)
900 = 900 HURRAH!
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