Question

use the diagram below to identify the given angle pairs. this is not an e - textbook problem. a vertical angles b linear pair

Explanation:

Step1: Recall vertical - angles definition

Vertical angles are opposite angles formed by the intersection of two lines.

Step2: Identify vertical - angle pairs

In the given diagram, $\angle1$ and $\angle3$ are vertical angles, $\angle2$ and $\angle4$ are vertical angles, $\angle5$ and $\angle7$ are vertical angles, $\angle6$ and $\angle8$ are vertical angles.

Step3: Recall linear - pair definition

A linear pair is a pair of adjacent angles whose non - common sides are opposite rays and the sum of the angles in a linear pair is $180^{\circ}$.

Step4: Identify linear - pair

$\angle1$ and $\angle2$ form a linear pair, $\angle3$ and $\angle4$ form a linear pair, $\angle5$ and $\angle6$ form a linear pair, $\angle7$ and $\angle8$ form a linear pair.

Answer:

Vertical angles: $\angle1$ and $\angle3$, $\angle2$ and $\angle4$, $\angle5$ and $\angle7$, $\angle6$ and $\angle8$.
Linear pairs: $\angle1$ and $\angle2$, $\angle3$ and $\angle4$, $\angle5$ and $\angle6$, $\angle7$ and $\angle8$.