Question

for the figure below, give the following. (a) one pair of angles that form a linear pair (b) one pair of vertical angles (c) one pair of angles that are congruent

Explanation:

Step1: Recall linear - pair definition

A linear pair of angles are adjacent angles that form a straight line. $\angle1$ and $\angle2$ are adjacent and their non - common sides form a straight line.

Step2: Recall vertical - angles definition

Vertical angles are the non - adjacent angles formed by two intersecting lines. $\angle1$ and $\angle3$ are vertical angles.

Step3: Recall congruent - angles concept

Vertical angles are congruent. So, $\angle1$ and $\angle3$ are congruent. Also, corresponding angles (e.g., $\angle1$ and $\angle5$) are congruent when two parallel lines are cut by a transversal. Here we can choose $\angle1$ and $\angle3$ as a pair of congruent angles.

Answer:

(a) $\angle1$ and $\angle2$
(b) $\angle1$ and $\angle3$
(c) $\angle1$ and $\angle3$