SOLUTION: One angle of a polygon is a right angle and the rest of the angles are each 135.How many sides does these polygon have?

Question 534115: One angle of a polygon is a right angle and the rest of the angles are each 135.How many sides does these polygon have?
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
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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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