Chapter 4.1, Problem 84E

a.

To determine

To find: The complement and supplement of given angle.

Answer to Problem 84E

Complement angle is $55°$ and supplement angle is $145°$ .

Explanation of Solution

Given Information: Angle is $35°$ .

Calculation:

Complement Angle:

  $\theta =90°-35°=55°$

Supplement Angle:

  ${\theta }_1=180°-35°=145°$

Thus, complement angle is $55°$ and supplement angle is $145°$ .

b.

To determine

To find: The complement and supplement of given angle.

Answer to Problem 84E

Complement angle doesn’t exist and supplement angle is $16°$ .

Explanation of Solution

Given Information: Angle is $164°$ .

Calculation:

Complement Angle:

As $164°$ is greater than $90°$ , there is no complement angle.

Supplement Angle:

  ${\theta }_1=180°-164°=16°$

Thus, complement angle doesn’t exist and supplement angle is $16°$ .

c.

To determine

To find: The complement and supplement of given angle.

Answer to Problem 84E

Complement and supplement angles don’t exist.

Explanation of Solution

Given Information: Angle is $4$ .

Calculation:

Complement Angle:

As angle is greater than $\frac{\pi }{2}$ , there is no complement angle.

Supplement Angle:

As angle is greater than $\pi$ , there is no supplement angle.

Thus, complement and supplement angles don’t exist.

d.

To determine

To find: The complement and supplement of given angle.

Answer to Problem 84E

Complement angle is $0.0708$ and supplement angle is $1.6416$ .

Explanation of Solution

Given Information: Angle is $\frac{3}{2}$ .

Calculation:

Complement Angle:

  $\theta =\frac{\pi }{2}-\frac{3}{2}=0.0708$

Supplement Angle:

  ${\theta }_1=\pi -\frac{3}{2}=1.6416$

Thus, complement angle is $0.0708$ and supplement angle is $1.6416$ .