SOLUTION: If the sum of the interior angles in a regular polygon is 3600o , then what is the value of each interior angle? How many sides does it have?

Question 1173719: If the sum of the interior angles in a regular polygon is 3600o
, then what is the value of each interior
angle? How many sides does it have?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13195) (Show Source): You can put this solution on YOUR website!

The sum of the measures of a polygon is 180(n-2), where n is the number of sides.

The polygon has 22 sides; the measure of each interior angle is 3600/22 degrees.

Answer by ikleyn(52747) (Show Source): You can put this solution on YOUR website!
.

For any convex polygon with n sides, the sum of interior angles is 180*(n-2) degrees. Since in your case this sum is 3600°, it gives you this equation 180*(n-2) = 3600. Divide it by 180 (both sides) to get n-2 = 3600/180 = 20; n = 20 + 2 = 22. So, your polygon has 22 sides. ANSWER

Solved.

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