SOLUTION: The measure of an interior angle of a regular polygon is three (3) times the measure of the exterior angle. How many sides does the polygon have? Is there a formula or something

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Question 408195: The measure of an interior angle of a regular polygon is three (3) times the measure of the exterior angle. How many sides does the polygon have? Is there a formula or something that needs to be used?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Let theta be the measure of the exterior angle, and 3%2Atheta be the measure of the interior angle. These two must add to 180 degree (since they're a linear pair) so

theta+%2B+3%2Atheta+=+180 --> theta+=+45, 3%2Atheta = 135.

Two ways to find the number of sides:

Solution 1:
If you know that the sum of the exterior angles of an n-gon is 360 degrees, and that in this case the exterior angle is 45 degrees, then the number of sides is 360/45 = 8.

Solution 2:
The sum of the measures of the interior angles of an n-gon is 180%28n-2%29. Divide this by n to get the average measure. Since each interior angle measures 135, we have

135+=+180%28n-2%29%2Fn, which can be solved to obtain n+=+8.