Chapter 7.4, Problem 2PSA

a

To determine

The measure of the exterior angles of the equiangular pentagon has to be found

Answer to Problem 2PSA

The measure of the exterior angles is ${72}^0$

Explanation of Solution

Given information : The polygon is a pentagon − with five sides.

We know the sum of the exterior angles is always ${360}^0$ . Thus, the measure of one angle will be

  $\frac{{360}^0}{n}$ , where n will be five in this case.

Thus, the measure of angle will be ${72}^0$

b

To determine

The measure of the exterior angles of the equiangular hexagon has to be found

Answer to Problem 2PSA

The measure of the exterior angles is ${60}^0$

Explanation of Solution

Given information : The polygon is a hexagon − with six sides.

We know the sum of the exterior angles is always ${360}^0$ . Thus, the measure of one angle will be

  $\frac{{360}^0}{n}$ , where n will be six in this case.

Thus, the measure of angle will be ${60}^0$

c

To determine

The measure of the exterior angles of the equiangular nonagon has to be found

Answer to Problem 2PSA

The measure of the exterior angles is ${20}^0$

Explanation of Solution

Given information : The polygon is a nonagon − with nine sides.

We know the sum of the exterior angles is always ${360}^0$ . Thus, the measure of one angle will be

  $\frac{{360}^0}{n}$ , where n will be nine in this case.

Thus, the measure of angle will be ${20}^0$

d

To determine

The measure of the exterior angles of the equiangular dodecagon has to be found

Answer to Problem 2PSA

The measure of the exterior angles is ${30}^0$

Explanation of Solution

Given information : The polygon is a dodecagon − with twelve sides.

We know the sum of the exterior angles is always ${360}^0$ . Thus, the measure of one angle will be

  $\frac{{360}^0}{n}$ , where n will be twelve in this case.

Thus, the measure of angle will be ${30}^0$

e

To determine

The measure of the exterior angles of the equiangular $21-gon$ has to be found

Answer to Problem 2PSA

The measure of the exterior angles is ${17.14}^0$

Explanation of Solution

Given information : The polygon is a $21-gon$ − with twenty-one sides.

We know the sum of the exterior angles is always ${360}^0$ . Thus, the measure of one angle will be

  $\frac{{360}^0}{n}$ , where n will be twenty-one in this case.

Thus, the measure of angle will be ${17.14}^0$