Exercise 3 Page 914

We want to determine the expression that best represents the degree measure of an interior angle of a regular polygon with n sides. To do so, we will use the given table.

We will substitute the number of sides for n into the given expressions. Then we will compare the results with the correct angle measures. We can start with the first line, which describes the relationship between the number of sides and the angle measures in triangles. Let's substitute 3 for n into the given expressions!

In case of triangles, when evaluating these expressions, we are supposed to obtain an angle measure of 60 degrees. Since the result in option A is not equal to 60, answer A is not correct. Now we can consider only three options: B, C, and D. Let's substitute 4 for n into these expressions.

For quadrilaterals, we are supposed to obtain an angle measure of 90 degrees after evaluating these expressions. Since the result in option B is not equal to 90, answer B is not correct. Therefore, we can consider only two options: C and D. Next, we will substitute 5 for n into these expressions.

For pentagons, we are supposed to get 108 degrees after evaluating these expressions. Since the angle measure in option D is not equal to 108, answer D is not correct. We can see that C is the only answer that can be correct. Let's check whether the expression from option C accurately finds the degree measure for hexagons, heptagons, and octagons.

After substituting 6, 7, and 8 into this expression, we obtained the correct values of angle measures. Since this expression best represents the degree measure of an interior angle of a regular polygon with n sides, the correct answer is C.