The sum of the measures of the exterior angles of a polygon, one angle at each vertex, is 360^(∘).
For example, consider the following polygon.
Based on the diagram, the relation below holds true.
m∠ 1 + m∠ 2 + m∠ 3 + m∠ 4 + m∠ 5+ m∠ 6 = 360^(∘)
In a regular polygon, all exterior angles have the same measure. For this reason, if a given value is a measure of an exterior angle of a regular polygon, then 360^(∘) divided by that value has to be an integer. Let's use this test on the given values.
Testing the Values
Let's test each of the given values by dividing 360^(∘) by them. If the result is not an integer, the value cannot be a measure of an exterior angle of a regular polygon.
Value
360^(∘)/Value
Integer?
18^(∘)
360^(∘)/18^(∘) = 20
Yes
24^(∘)
360^(∘)/24^(∘) = 15
Yes
28^(∘)
360^(∘)/28^(∘) = 12.857142...
No
40^(∘)
360^(∘)/40^(∘) = 9
Yes
We see that 28^(∘) cannot be a measure of an exterior angle of a regular polygon. Therefore, C is the correct answer.
