Question

Which of the following could be an interior angle measure of a regular polygon?

Answer 1

Correct answer is C.

Formula for the sum of interior angles of a regular polygon is $S_n=(n-2)180^o$, where $S_n$ is the sum of interior angles and $n$ is the number of sides of the regular polygon. Check by substituting the given values.

The measure of an interior angle of a regular polygon is equal to $\frac{S_n}{n}$.

The equation $\frac{S_n}{n}=\alpha$, where $\alpha$ is the measure of the interior angle of a regular polygon, must have positive integer solution for n. Check for $\alpha=150^o$.

$\frac{S_n}{n}=150^o \\\frac{(n-2)180^o}{n}=150^o \\(n-2)180^o=150^on \\180^on-360^o=150^on \\30^on=360^o \\n= \frac{360^o}{30^o} \\n=12$