Chapter 4.1, Problem 86E

a.

To determine

To find: The complement and supplement of each angle.

Answer to Problem 86E

It has no complement angle and no supplement angle.

Explanation of Solution

Given information: Given angle is ${220}^{\circ }$ .

Calculation: Given angle is ${220}^{\circ }$ .

It has no complement angle because ${220}^{\circ }$ is greater than ${90}^{\circ }$ .

It has no supplement angle because ${220}^{\circ }$ is greater than ${180}^{\circ }$ .

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

b.

To determine

To find: The complement and supplement of each angle.

Answer to Problem 86E

Thus, complement angle is ${52}^{\circ }$ and supplement angle is ${142}^{\circ }$ .

Explanation of Solution

Given information: Given angle is ${38}^{\circ }$ .

Calculation: Given angle is ${38}^{\circ }$ .

Complement angle of ${38}^{\circ }$ is ${90}^{\circ }-{38}^{\circ }={52}^{\circ }$ .

Supplement angle of ${38}^{\circ }$ is ${180}^{\circ }-{38}^{\circ }={142}^{\circ }$ .

Thus, complement angle is ${52}^{\circ }$ and supplement angle is ${142}^{\circ }$ .

c.

To determine

To find: The complement and supplement of each angle.

Answer to Problem 86E

The complement angle is $\frac{\pi }{3}$ and supplement angle is $\frac{5\pi }{6}$ .

Explanation of Solution

Given information: Given angle is $\frac{\pi }{6}$ .

Calculation: Given angle is $\frac{\pi }{6}$ .

Complement angle of $\frac{\pi }{6}$ is $\frac{\pi }{2}-\frac{\pi }{6}=\frac{3\pi -1\pi }{6}=\frac{2\pi }{6}=\frac{\pi }{3}$ .

Supplement angle of $\frac{\pi }{8}$ is $\pi -\frac{\pi }{6}=\frac{6\pi -\pi }{6}=\frac{5\pi }{6}$ .

Thus, the complement angle is $\frac{\pi }{3}$ and supplement angle is $\frac{5\pi }{6}$ .

d.

To determine

To find: The complement and supplement of each angle.

Answer to Problem 86E

It has no complement angle but supplement angle is $\frac{3\pi }{7}$ ..

Explanation of Solution

Given information: Given angle is $\frac{4\pi }{7}$ .

Calculation: Given angle is $\frac{4\pi }{7}$ .

It has no complement angle because $\frac{4\pi }{7}$ is greater than $\frac{\pi }{2}$ .

Supplement angle of $\frac{4\pi }{7}$ is $\pi -\frac{4\pi }{7}=\frac{7\pi -4\pi }{7}=\frac{3\pi }{7}$ .

Thus, it has no complement angle but supplement angle is $\frac{3\pi }{7}$ .