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 supplementary

Explanation:

Step1: Recall linear - pair definition

A linear pair of angles are adjacent angles that form a straight - line. In the given figure, $\angle1$ and $\angle2$ form a linear pair since they 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 as they are formed by the intersection of two lines and are non - adjacent.

Step3: Recall supplementary angles definition

Supplementary angles are two angles whose sum is $180^{\circ}$. A linear pair of angles is always supplementary. Also, $\angle1$ and $\angle5$ are supplementary (corresponding angles with parallel lines and they can also be considered in terms of the straight - line formed by the transversal and the parallel lines).

Answer:

(a) $\angle1$ and $\angle2$
(b) $\angle1$ and $\angle3$
(c) $\angle1$ and $\angle5$