Chapter 4.1, Problem 85E

a.

To determine

To find: The complement and supplement of each angle.

Answer to Problem 85E

It has no complement angle, but its supplement angle is ${87}^{\circ }$ .

Explanation of Solution

Given information: Given angle is ${93}^{\circ }$ .

Calculation: Given angle is ${93}^{\circ }$ .

It has no complement angle because ${93}^{\circ }$ is greater than ${90}^{\circ }$ .

Supplement angle of ${93}^{\circ }$ is ${180}^{\circ }-{93}^{\circ }={87}^{\circ }$ .

Thus, it has no complement angle, but its supplement angle is ${87}^{\circ }$ .

b.

To determine

To find: The complement and supplement of each angle.

Answer to Problem 85E

Thus, complement angle is ${70}^{\circ }$ and supplement angle is ${160}^{\circ }$ .

Explanation of Solution

Given information: Given angle is ${20}^{\circ }$ .

Calculation: Given angle is ${20}^{\circ }$ .

The complement angle of ${20}^{\circ }$ is ${90}^{\circ }-{20}^{\circ }={70}^{\circ }$ .

The supplement angle of ${20}^{\circ }$ is ${180}^{\circ }-{20}^{\circ }={160}^{\circ }$ .

Thus, the complement angle is ${70}^{\circ }$ and supplement angle is ${160}^{\circ }$ .

c.

To determine

To find: The complement and supplement of each angle.

Answer to Problem 85E

The complement angle is $\frac{3\pi }{8}$ and supplement angle is $\frac{7\pi }{8}$ .

Explanation of Solution

Given information: Given angle is $\frac{\pi }{8}$ .

Calculation: Given angle is $\frac{\pi }{8}$ .

Complement angle of $\frac{\pi }{8}$ is $\frac{\pi }{2}-\frac{\pi }{8}=\frac{4\pi -1\pi }{8}=\frac{3\pi }{8}$ .

Supplement angle of $\frac{\pi }{8}$ is $\pi -\frac{\pi }{8}=\frac{8\pi -\pi }{8}=\frac{7\pi }{8}$ .

Thus, the complement angle is $\frac{3\pi }{8}$ and supplement angle is $\frac{7\pi }{8}$ .

d.

To determine

To find: The complement and supplement of each angle.

Answer to Problem 85E

It has no complement angle and no supplement angle.

Explanation of Solution

Given information: Given angle is $4\pi$ .

Calculation: Given angle is $4\pi$ .

It has no complement angle because $4\pi$ is greater than $\frac{\pi }{2}$ .

It has no supplement angle because $4\pi$ is greater than $\pi$ .

Thus, it has no complement angle and no supplement angle.