Chapter 49, Problem 22A

To determine

(a)

To find out the supplements of the following angles.

Answer to Problem 22A

  $x=167°$.

Explanation of Solution

Given information:

The given angle is ${13}^{\circ }$.

Calculation:

  $$ Two angles are Supplementary when they add up to $\text{18}0°$ degrees. These two are supplementary because

  $\begin{array}{l}\Rightarrow 13°+\text{ x }=\text{ 18}0°\\ \Rightarrow x=167°\end{array}$

To determine

(b)

To find out the supplements of the following angles.

Answer to Problem 22A

  $x=115°$.

Explanation of Solution

Given information:

The given angle is ${65}^{\circ }$.

Calculation:

  $$ Two angles aresupplements when they add up to $\text{18}0°$ degrees.These two are complementary because

  $\begin{array}{l}\Rightarrow 65°+\text{ x }=\text{ 18}0°\\ \Rightarrow x=115°\end{array}$

To determine

(c)

To find out the supplements of the following angles.

Answer to Problem 22A

  $x=89°$

Explanation of Solution

Given information:

The given angle is ${91}^{\circ }$.

Calculation:

  $$ Two angles aresupplements when they add up to $\text{18}0°$ degrees.These two are supplements because

  $\begin{array}{l}\Rightarrow 91°+\text{ x }=\text{ 18}0°\\ \Rightarrow x=89°\end{array}$

To determine

(d)

To find out the supplements of the following angles.

Answer to Problem 22A

  $x=0°$.

Explanation of Solution

Given information:

The given angle is ${179}^{\circ }59\text{'}$.

Calculation:

  $$ Two angles aresupplements when they add up to $\text{18}0°$ degrees.These two are supplements because

  $\begin{array}{l}\Rightarrow 179°59\text{'}+\text{ x }=\text{ 18}0°\\ \Rightarrow x=0°\end{array}$

To determine

(e)

To find out the supplements of the following angles.

Answer to Problem 22A

  $x=179°11\text{'}$.

Explanation of Solution

Given information:

The given angle is $0^{\circ }49\text{'}$.

Calculation:

  $$ Two angles aresupplements when they add up to $\text{18}0°$ degrees.These two are supplements because

  $\begin{array}{l}\Rightarrow 0°49\text{'}+\text{ x }=\text{ 18}0°\\ \Rightarrow x=179°11\text{'}\end{array}$

To determine

(f)

To find out the supplements of the following angles.

Answer to Problem 22A

  $x=90°01\text{'}$.

Explanation of Solution

Given information:

The given angle is ${89}^{\circ }59\text{'}$.

Calculation:

  $$ Two angles aresupplements when they add up to $\text{18}0°$ degrees.These two are supplements because

  $\begin{array}{l}\Rightarrow 89°59\text{'}+\text{ x }=\text{ 18}0°\\ \Rightarrow x=90°01\text{'}\end{array}$

To determine

(g)

To find out the supplements of the following angles.

Answer to Problem 22A

  $x=177°16\text{'}40"$.

Explanation of Solution

Given information:

The given angle is $2^{\circ }43\text{'}20"$.

Calculation:

  $$ Two angles aresupplements when they add up to $\text{18}0°$ degrees.These two are supplements because

  $\begin{array}{l}\Rightarrow 2°43\text{'}20"+\text{ x }=\text{ 18}0°\\ \Rightarrow x=177°16\text{'}40"\end{array}$

To determine

(h)

To find out the supplements of the following angles.

Answer to Problem 22A

  $x=111°38\text{'}31"$.

Explanation of Solution

Given information:

The given angle is $x=68°21\text{'}29"$.

Calculation:

  $$ Two angles aresupplements when they add up to $\text{18}0°$ degrees.These two aresupplements because

  $\begin{array}{l}\Rightarrow 68°21\text{'}29"+\text{ x }=\text{ 18}0°\\ \Rightarrow x=111°38\text{'}31"\end{array}$

To determine

(i)

To find out the supplements of the following angles.

Answer to Problem 22A

  $x=149°27\text{'}52"$.

Explanation of Solution

Given information:

The given angle is ${133}^{\circ }32\text{'}08"$.

Calculation:

  $$ Two angles aresupplements when they add up to $\text{18}0°$ degrees.These two are supplements because

  $\begin{array}{l}\Rightarrow {133}^{\circ }32\text{'}08"+\text{ x }=\text{ 18}0°\\ \Rightarrow x=149°27\text{'}52"\end{array}$