Question

2.) the figure to the right shows lines that intersect at point o.
a. name a pair of vertical angles.

b. name a pair of supplementary angles.

Explanation:

Part a

Vertical angles are formed when two lines intersect, and they are opposite each other. In the figure, lines \(AB\) and \(CD\) intersect at \(O\), and lines \(EP\) is also intersecting at \(O\). A pair like \(\angle AOC\) and \(\angle BOD\) are vertical angles (or other pairs like \(\angle AOD\) and \(\angle BOC\), \(\angle AOE\) and \(\angle PO D\) etc., but we can choose one).

Supplementary angles are two angles whose sum is \(180^\circ\). When two lines intersect, adjacent angles on a straight line are supplementary. For example, \(\angle AOC\) and \(\angle COE\) (if \(EP\) is a straight line, but also pairs like \(\angle AOC\) and \(\angle AOD\) since they form a linear pair, or \(\angle AOE\) and \(\angle AOP\) as \(EP\) is a straight line). Let's take \(\angle AOC\) and \(\angle AOD\) as they are adjacent and form a linear pair (sum to \(180^\circ\)).

Answer:

\(\angle AOC\) and \(\angle BOD\) (other valid pairs are also acceptable)

Part b