Chapter 9, Problem 1T

Consider a ${42}^{\circ }$ angle. Answer each of the following.

(a) What is the measure of its complement?

(b) What is the measure of its supplement?

(c) Classify it as acute, obtuse, right, or straight.

To determine

To calculate: The complement angle when angle is $42°$.

Answer to Problem 1T

Solution:

The complement angle is $\angle B=48°$.

Explanation of Solution

Given:

The angle,$42°$.

Calculation:

Complementary angles are two angles. whose sum is $90°$ degrees.

It’s mean $\angle A=42°$. Substitutes in $\angle A+\angle B=90°$.

$\begin{array}{c}\angle A+\angle B=90°\\ 42°+\angle B=90°\\ \angle B=90°-42°\\ \angle B=48°\end{array}$

Hence, the angle is $\angle B=48°$ , when it is a complement.

To determine

To calculate: The supplement angle when angle is $42°$.

Answer to Problem 1T

Solution:

The supplement angle is $\angle B=138°$.

Explanation of Solution

Given:

The angle,$42°$.

Calculation:

Supplementary angles are two angles, whose sum is $180°$ degrees.

It means:

$\begin{array}{c}\angle A+\angle B=180°\\ 42°+\angle B=180°\\ \angle B=180°-42°\\ =138°\end{array}$

Hence, the angle $\angle B=138°$ for supplement.

To determine

The angle is acute, obtuse, right, or straight.

Answer to Problem 1T

Solution:

The angle is acute angle.

Given:

The angle,$42°$.

Explanation of Solution

It is an acute angle because acute angles are those which are less than $90°$. So, the angle $42°$ is an acute angle.

Hence, it is an acute angle.