Chapter 4.1, Problem 32E

a.

To determine

To find : The complement and supplement of ${46}^{°}$

Answer to Problem 32E

Complement of ${46}^{°}$ is ${44}^{°}$

Supplement of ${46}^{°}$ is ${134}^{°}$

Explanation of Solution

Given information:

The degree measure of angle is ${46}^{°}$

Concept and Formula Used:

Complementary angles- Pair of angles with sum equal to ${90}^{°}$

Supplementary angles- Pair of angles with sum equal to ${180}^{°}$

Calculation:

The measure of the angle is ${46}^{°}$ .

Complement of angle is $={90}^{°}-{46}^{°}={44}^{°}$

Supplement of angle is $={180}^{°}-{46}^{°}={134}^{°}$

Conclusion:

Complement of ${46}^{°}$ is ${44}^{°}$

Supplement of ${46}^{°}$ is ${134}^{°}$

b.

To determine

To find : The complement and supplement of ${93}^{°}$

Answer to Problem 32E

Complement of ${93}^{°}$ not exist.

Supplement of ${93}^{°}$ is ${87}^{°}$

Explanation of Solution

Given information:

The degree measure of angle is ${93}^{°}$

Concept and Formula Used:

Complementary angles- Pair of angles with sum equal to ${90}^{°}$

Supplementary angles- Pair of angles with sum equal to ${180}^{°}$

Calculation:

The measure of the angle is ${93}^{°}$ .

As ${93}^{°}$ is greater than ${90}^{°}$ therefore complement of angle not exist

Supplement of angle is $={180}^{°}-{93}^{°}={87}^{°}$

Conclusion:

Complement of ${93}^{°}$ not exist.

Supplement of ${93}^{°}$ is ${87}^{°}$