Chapter 7.4, Problem 4PSA

a

To determine

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

Answer to Problem 4PSA

The number of sides is $10$

Explanation of Solution

Given information : The value of each angle is $A={144}^0$

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

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

Thus, the interior angle will be

  $A={180}^0-\frac{{360}^0}{n}$

Thus, the value of n will be $10$

b

To determine

The number of sides of the equiangular polygon has to be found using the value of each angle given as mentioned

Answer to Problem 4PSA

The number of sides is $6$

Explanation of Solution

Given information : The value of each angle is $A={120}^0$

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

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

Thus, the interior angle will be

  $A={180}^0-\frac{{360}^0}{n}$

Thus, the value of n will be $6$

c

To determine

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

Answer to Problem 4PSA

The number of sides is $15$

Explanation of Solution

Given information : The value of each angle is $A={156}^0$

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

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

Thus, the interior angle will be

  $A={180}^0-\frac{{360}^0}{n}$

Thus, the value of n will be $15$

d

To determine

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

Answer to Problem 4PSA

The number of sides is $20$

Explanation of Solution

Given information : The value of each angle is $A={162}^0$

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

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

Thus, the interior angle will be

  $A={180}^0-\frac{{360}^0}{n}$

Thus, the value of n will be $20$

e

To determine

The number of sides of the equiangular polygon has to be found by using the relevant data

Answer to Problem 4PSA

The number of sides is $50$

Explanation of Solution

Given information : The value of each angle is $A={172.8}^0$

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

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

Thus, the interior angle will be

  $A={180}^0-\frac{{360}^0}{n}$

Thus, the value of n will be $50$