Chapter 4.1, Problem 19E

a.

To determine

To find:The complement and supplement of angle 1.

Answer to Problem 19E

The complement and supplement of angle $1$ are $0.57$ and $2.14$ , respectively.

Explanation of Solution

Given information:

The give angle is $1$ .

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.

  $\begin{array}{c}\frac{\pi }{2}-1=\frac{3.14}{2}-1\\ =1.57-1\\ \approx 0.57\end{array}$

Calculate the supplement angle.

  $\begin{array}{c}\pi -1=3.14-1\\ \approx 2.14\end{array}$

Therefore, the complement and supplement of angle $1$ are $0.57$ and $2.14$ , respectively.

b.

To determine

To find:The complement and supplement of angle $2$ .

Answer to Problem 19E

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

Explanation of Solution

Given information:

The give angle is $2$ .

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, 2 is greater than $\frac{\pi }{2}$ and it gives negative value. A complement angle cannot be negative.

Calculate the supplement angle.

  $\begin{array}{c}\pi -2=3.14-2\\ \approx 1.14\end{array}$

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