Chapter 7, Problem 16RP

To determine

The name of the regular polygon is to be found

Answer to Problem 16RP

The regular polygon is a triangle

Explanation of Solution

Given information : The following information is given

Measure of an exterior angle is twice the interior angle

We know that for any regular polygon, the measure of interior can be calculated as

  $x=\frac{n-2({180}^0)}{n}$ , where n is the number of sides of the polygon

Now, the exterior angle can be calculated as

  $e={180}^0-x={180}^0-\frac{n-2({180}^0)}{n}$

Now, we are given that

  $e=2x$

Thus, substituting the values of x and e from the equations we built, we get

  $n=3$

Now, for $n=3$ , we know that the polygon is a triangle.