Correct answer is C.
Formula for the sum of interior angles of a regular polygon is [tex]S_n=(n-2)180^o[/tex], where [tex]S_n[/tex] is the sum of interior angles and [tex]n[/tex] 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 [tex] \frac{S_n}{n} [/tex].
The equation [tex] \frac{S_n}{n}=\alpha [/tex], where [tex]\alpha[/tex] is the measure of the interior angle of a regular polygon, must have positive integer solution for n. Check for [tex]\alpha=150^o[/tex].
[tex]\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 [/tex]
