for the figure below, give the following. (a) one pair of vertical angles (b) one pair of angles that form a…

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are opposite angles formed by the intersection of two lines. In the given figure, $\angle1$ and $\angle4$ are vertical angles (or $\angle2$ and $\angle3$, $\angle5$ and $\angle8$, $\angle6$ and $\angle7$).

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 (or $\angle2$ and $\angle4$, $\angle4$ and $\angle3$, $\angle3$ and $\angle1$, $\angle5$ and $\angle6$, $\angle6$ and $\angle8$, $\angle8$ and $\angle7$, $\angle7$ and $\angle5$).

Step3: Recall supplementary - angle definition

Supplementary angles are two angles whose sum is $180^{\circ}$. A linear - pair of angles are supplementary. So, $\angle1$ and $\angle2$ are supplementary (any linear - pair will work).

Answer:

(a) $\angle1$ and $\angle4$ (b) $\angle1$ and $\angle2$ (c) $\angle1$ and $\angle2$