Question

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

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are formed when two lines intersect. They are opposite each other. In the given figure, \(\angle1\) and \(\angle3\) are vertical angles.

Step2: Recall linear - pair definition

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

Step3: Recall congruent - angle concept

Vertical angles are congruent. So \(\angle1\) and \(\angle3\) are congruent (also, vertical angles \(\angle5\) and \(\angle7\) etc. are congruent). We can choose \(\angle1\) and \(\angle3\) as a pair of congruent angles.

Answer:

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