Exercise 47 Page 562

We want to find which of the following values cannot be the measure of an exterior angle of a regular polygon. &A 28^(∘)&&B 24^(∘) &&C 28^(∘)&&D40^(∘) To do so, let's first recall that the Polygon Exterior Angles Theorem.

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.

We see that 28^(∘) cannot be a measure of an exterior angle of a regular polygon. Therefore, C is the correct answer.