Chapter 7.4, Problem 1PSA

a

To determine

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

Answer to Problem 1PSA

The measure of the exterior angles is ${120}^0$

Explanation of Solution

Given information : The polygon is a triangle − with three 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 three in this case.

Thus, the measure of angle will be ${120}^0$

b

To determine

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

Answer to Problem 1PSA

The measure of the exterior angles is ${90}^0$

Explanation of Solution

Given information : The polygon is a quadrilateral − with four 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 four in this case.

Thus, the measure of angle will be ${90}^0$

c

To determine

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

Answer to Problem 1PSA

The measure of the exterior angles is ${45}^0$

Explanation of Solution

Given information : The polygon is a octagon − with eight 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 eight in this case.

Thus, the measure of angle will be ${45}^0$

d

To determine

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

Answer to Problem 1PSA

The measure of the exterior angles is ${24}^0$

Explanation of Solution

Given information : The polygon is a pentadecagon − with fifteen 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 fifteen in this case.

Thus, the measure of angle will be ${24}^0$

e

To determine

The measure of the exterior angles of the equiangular $23-gon$ has to be found

Answer to Problem 1PSA

The measure of the exterior angles is ${15.65}^0$

Explanation of Solution

Given information : The polygon is a $23-gon$ − with twenty three 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 three in this case.

Thus, the measure of angle will be ${15.65}^0$