Chapter 4.1, Problem 31E

a.

To determine

To find : The complement and supplement of ${18}^{°}$

Answer to Problem 31E

Complement of ${18}^{°}$ is ${72}^{°}$

Supplement of ${18}^{°}$ is ${162}^{°}$

Explanation of Solution

Given information:

The degree measure of angle is ${18}^{°}$

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 ${18}^{°}$ .

Complement of angle is $={90}^{°}-{18}^{°}={72}^{°}$

Supplement of angle is $={180}^{°}-{18}^{°}={162}^{°}$

Conclusion:

Complement of ${18}^{°}$ is ${72}^{°}$

Supplement of ${18}^{°}$ is ${162}^{°}$

b.

To determine

To find : The complement and supplement of ${85}^{°}$

Answer to Problem 31E

Complement of ${85}^{°}$ is $5^{°}$

Supplement of ${85}^{°}$ is ${95}^{°}$

Explanation of Solution

Given information:

The degree measure of angle is ${85}^{°}$

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 ${85}^{°}$ .

Complement of angle is $={90}^{°}-{85}^{°}=5^{°}$

Supplement of angle is $={180}^{°}-{85}^{°}={95}^{°}$

Conclusion:

Complement of ${85}^{°}$ is $5^{°}$

Supplement of ${85}^{°}$ is ${95}^{°}$