Chapter 49, Problem 21A

To determine

(a)

To find out the complements of the following angles.

Answer to Problem 21A

  $x=56°$.

Explanation of Solution

Given information:

The given angle is ${43}^{\circ }$.

Calculation:

  $$ Two angles are complementary when they add up to $\text{9}0°$ degrees.These two are complementary because

  $\begin{array}{l}\Rightarrow 43°+\text{ x }=\text{ 9}0°\\ \Rightarrow x=56°\end{array}$

To determine

(b)

To find out the complements of the following angles.

Answer to Problem 21A

  $x=14°$.

Explanation of Solution

Given information:

The given angle is ${76}^{\circ }$.

Calculation:

  $$ Two angles are complementary when they add up to $\text{9}0°$ degrees.These two are complementary because

  $\begin{array}{l}\Rightarrow {76}^{\circ }+\text{ x }=\text{ 9}0°\\ \Rightarrow x=14°\end{array}$

To determine

(c)

To find out the complements of the following angles.

Answer to Problem 21A

  $x=73°$

Explanation of Solution

Given information:

The given angle is ${17}^{\circ }$.

Calculation:

  $$ Two angles are complementary when they add up to $\text{9}0°$ degrees.These two are complementary because

  $\begin{array}{l}\Rightarrow {17}^{\circ }+\text{ x }=\text{ 9}0°\\ \Rightarrow x=73°\end{array}$

To determine

(d)

To find out the complements of the following angles.

Answer to Problem 21A

  $x=85°$.

Explanation of Solution

Given information:

The given angle is $5^{\circ }$.

Calculation:

  $$ Two angles are complementary when they add up to $\text{9}0°$ degrees.These two are complementary because

  $\begin{array}{l}\Rightarrow 5°+\text{ x }=\text{ 9}0°\\ \Rightarrow x=85°\end{array}$

To determine

(e)

To find out the complements of the following angles.

Answer to Problem 21A

  $x=22°11\text{'}$.

Explanation of Solution

Given information:

The given angle is ${67}^{\circ }49\text{'}$.

Calculation:

  $$ Two angles are complementary when they add up to $\text{9}0°$ degrees.These two are complementary because

  $\begin{array}{l}\Rightarrow 67°49\text{'}+\text{ x }=\text{ 9}0°\\ \Rightarrow x=22°11\text{'}\end{array}$

To determine

(f)

To find out the complements of the following angles.

Answer to Problem 21A

  $x=44°41\text{'}$.

Explanation of Solution

Given information:

The given angle is ${45}^{\circ }19\text{'}$.

Calculation:

  $$ Two angles are complementary when they add up to $\text{9}0°$ degrees.These two are complementary because

  $\begin{array}{l}\Rightarrow 45°19\text{'}+\text{ x }=\text{ 9}0°\\ \Rightarrow x=44°41\text{'}\end{array}$

To determine

(g)

To find out the complements of the following angles.

Answer to Problem 21A

  $x=68°17\text{'}$.

Explanation of Solution

Given information:

The given angle is ${21}^{\circ }43\text{'}$.

Calculation:

  $$ Two angles are complementary when they add up to $\text{9}0°$ degrees.These two are complementary because

  $\begin{array}{l}\Rightarrow 21°43\text{'}+\text{ x }=\text{ 9}0°\\ \Rightarrow x=68°17\text{'}\end{array}$

To determine

(h)

To find out the complements of the following angles.

Answer to Problem 21A

  $x=11°40\text{'}33"$.

Explanation of Solution

Given information:

The given angle is ${78}^{\circ }19\text{'}27"$.

Calculation:

  $$ Two angles are complementary when they add up to $\text{9}0°$ degrees.These two are complementary because

  $\begin{array}{l}\Rightarrow 78°19\text{'}27"+\text{ x }=\text{ 9}0°\\ \Rightarrow x=11°40\text{'}33"\end{array}$

To determine

(i)

To find out the complements of the following angles.

Answer to Problem 21A

  $x=30°59\text{'}1"$.

Explanation of Solution

Given information:

The given angle is ${59}^{\circ }0\text{'}59"$.

Calculation:

  $$ Two angles are complementary when they add up to $\text{9}0°$ degrees.These two are complementary because

  $\begin{array}{l}\Rightarrow 59°0\text{'}59"+\text{ x }=\text{ 9}0°\\ \Rightarrow x=30°59\text{'}1"\end{array}$