Exercise 1 Page 452

Let's find the sum of the measures of interior angles, the measure of an interior angle, and an exterior angle of the given regular polygon one at a time.

Sum of the Measures of Interior Angles

The formula to find the sum of the measures of interior angles is ( n-2)180. To find the sum of the measures of the interior of a 30-gon, we will substitute 30 for n in this formula. ( 30 - 2)180 = 5040

Measure of Interior Angle

Recall that the measure of each interior angle of a regular n -gon is ( n-2)180 n. To find the measure of an interior angle of a 30 -gon, we have to substitute 30 for n in this expression. ( 30-2)180/30= 168

Measure of Exterior Angle

To find the measure of an exterior angle, notice that the interior and exterior angles of any polygon form a linear pair.

This means that their measures add to 180. Let's call the exterior angle of our regular polygon x. To find x, we can write an equation using the measure of the interior angle and the fact that these will add to 180. 168+x=180 ⇔ x=12 The measure of the exterior angle is 12.