SOLUTION: What is the measure of an interior angle in a regular polygon with 15 sides?

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Question 1151125: What is the measure of an interior angle in a regular polygon with 15 sides?
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
For an n-sided polygon there are n-2 triangles.
The sum of the interior angles is therefore 180%28n-2%29
In a 15-sided polygon:
Sum interior angles = 180%2815-2%29=180%2A13=2340°
Each interior angle of the regular polygon = 2340%2F15=156°

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

What is the measure of an interior angle in a regular polygon with 15 sides?
It's as SIMPLE as this:

The sum of the exterior angles of ANY polygon is 360o. With this being a REGULAR 15-sided polygon, each EXTERIOR angle = matrix%281%2C3%2C+360%2F15%2C+%22=%22%2C+24%5Eo%29

Therefore, EACH interior angle = highlight_green%28matrix%281%2C3%2C+180%5Eo+-+24%5Eo%2C+%22=%22%2C+156%5Eo%29%29

That's it! Nothing COMPLICATED and/or time-consuming!