Question

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

A.
45_
B.
72_
C.
150_
D.
173_

Answer 1

150

Explanation:

also edge2020

Answer 2

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
`(S_n)/(n)`.

The equation
`(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`.


`(S_n)/(n)=150^o \\((n-2)180^o)/(n)=150^o \\(n-2)180^o=150^on \\180^on-360^o=150^on \\30^on=360^o \\n= (360^o)/(30^o) \\n=12`