Question

critical thinking tell whether the statement is always, sometimes, or never true.
always sometimes never
angles in a linear pair are supplements of each other.
explain your reasoning.
a linear pair forms a straight angle, so the two angles will add to 180°.
angles that form a linear pair may have a sum that is 180° or less.
angles that form a linear pair may have a sum that is 180° or more.
it depends on the angles formed with the common side.

Explanation:

Step1: Recall linear pair definition

A linear pair of angles is formed when two adjacent angles are formed by two intersecting lines, and they form a straight line (a straight angle, which measures \(180^\circ\)).

Step2: Recall supplementary angles definition

Supplementary angles are two angles whose sum is \(180^\circ\).

Step3: Relate linear pair and supplementary angles

Since a linear pair forms a straight angle (sum of angles is \(180^\circ\)), the two angles in a linear pair must always add up to \(180^\circ\), meaning they are always supplementary.

Step4: Evaluate reasoning options

• The first reasoning option: "A linear pair forms a straight angle, so the two angles will add to \(180^\circ\)." is correct because it aligns with the definitions of linear pair and supplementary angles.
• The other options are incorrect: A linear pair's sum is always \(180^\circ\) (not "may be" or "depends"), so the other reasoning choices are wrong.

Answer:

For the first part (whether the statement is always, sometimes, or never true): Always (select the "Always" option).
For the reasoning: The option "A linear pair forms a straight angle, so the two angles will add to \(180^\circ\)."