Chapter 4.3, Problem 56SPR

To determine

Whether the given statement is always, sometimes or never true.

Answer to Problem 56SPR

Sometimes true.

Explanation of Solution

Given:

The given statement is:

Two angles that form a linear pair are supplementary.

Calculation:

In supplementary angles, the sum of measures of two angles in 180.

Let angle 1 and angle 2 be supplementary.

Then, $m\angle 1+m\angle 2=180$ .

If measure of angle 1 is less than 90, then;

  $\begin{array}{l}m\angle 2=180-m\angle 1\\ m\angle 2>180-90\\ m\angle 2=90\end{array}$

Here, angle 1 is acute and angle 2 is obtuse.

If measure of angle 1 is 90, then;

  $\begin{array}{l}m\angle 2=180-m\angle 1\\ m\angle 2=180-90\\ m\angle 2=90\end{array}$

Here, angle 1 and angle 2, both are right angles.

Hence, the statement is sometimes true.