Chapter 7.4, Problem 3PSA

a

To determine

The number of sides of the equiangular polygon has to be found

Answer to Problem 3PSA

The number of sides is $6$

Explanation of Solution

Given information : The value of each exterior angle is ${60}^0$

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 our answer in this case.

Thus, the value of n will be $6$

b

To determine

The number of sides of the given equiangular polygon has to be found out

Answer to Problem 3PSA

The number of sides is $9$

Explanation of Solution

Given information : The value of each exterior angle is ${40}^0$

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 our answer in this case.

Thus, the value of n will be $9$

c

To determine

The number of sides of the equiangular polygon with the given details is to be found

Answer to Problem 3PSA

The number of sides is $10$

Explanation of Solution

Given information : The value of each exterior angle is ${36}^0$

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 our answer in this case.

Thus, the value of n will be $10$

d

To determine

The number of sides of the equiangular polygon has to be found by using the details given

Answer to Problem 3PSA

The number of sides is $180$

Explanation of Solution

Given information : The value of each exterior angle is $2^0$

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 our answer in this case.

Thus, the value of n will be $180$

e

To determine

The number of sides of the equiangular polygon has to be found by the help of the given data

Answer to Problem 3PSA

The number of sides is $48$

Explanation of Solution

Given information : The value of each exterior angle is ${7.5}^0$

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 our answer in this case.

Thus, the value of n will be $48$