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