Question

The name may not be used a lot, but a 19-sided figure is called an enneadecagon. Either pronounce it 19 times in a row quickly, or calculate the sum of its interior angles. Since we cannot grade your speech, please calculate the sum of its interior angles in degrees?

Solution

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The sum of the measure of the interior angles of a polygon with nn sides is:

sum of interior angles=180°(n2)(1)\text{sum of interior angles}=180\text{\textdegree}(n-2) \color{white}\tag{1}

For an enneadecagon, as given, n=19n=19 so:

sum of interior angles=180°(192)=180°(17)=3060°\text{sum of interior angles}=180\text{\textdegree}(19-2)= 180\text{\textdegree}(17)= \color{#c34632}3060\text{\textdegree}

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