Chapter 4.1, Problem 20E

a.

To determine

Tofind:Thecomplement and supplement of angle 3.

Answer to Problem 20E

The complement angle of 3is not possible and the supplement angle is 0.14.

Explanation of Solution

Given information:

The give angle is3.

Calculation:

Two angles are complements of each other when their sum is $\frac{\pi }{2}$ . To determine the complement angle, subtract the given angle from $\frac{\pi }{2}$ .

Two angles are supplements of each other when their sum is $\pi$ . To determine the supplement angle, subtract the given angle from $\pi$ .

Since, 3is greater than $\frac{\pi }{2}$ and it gives negative value. A complement angle cannot be negative. So, it’s complement angle is not possible.

Calculate the supplement angle.

  $\begin{array}{c}\pi -1=3.14-3\\ \approx 0.14\end{array}$

Therefore, the complement angle of 2 is not possible and the supplement angle is 1.14.

b.

To determine

Tofind:The complement and supplement of angle 1.5.

Answer to Problem 20E

The complement and supplement of angle 1.5 are $0.07$ and $1.64$ , respectively.

Explanation of Solution

Given information:

The give angle is 1.5.

Calculation:

Two angles are complements of each other when their sum is $\frac{\pi }{2}$ . To determine the complement angle, subtract the given angle from $\frac{\pi }{2}$ .

Two angles are supplements of each other when their sum is $\pi$ . To determine the supplement angle, subtract the given angle from $\pi$ .

Calculate the complement angle.

  $\begin{array}{c}\frac{\pi }{2}-1=\frac{3.14}{2}-1.5\\ =1.57-1.5\\ \approx 0.07\end{array}$

Calculate the supplement angle.

  $\begin{array}{c}\pi -1.5=3.14-1\\ \approx 1.64\end{array}$

Therefore, the complement and supplement of angle 1.5 are $0.07$ and $1.64$ , respectively.