Question

name two pairs of congruent angles in the figure. justify your answers. name one pair of congruent angles. choose the correct answer below. a. ∠aob and ∠aod b. ∠boc and ∠aob c. ∠aod and ∠boc d. ∠aod and ∠aoc

Explanation:

Step1: Recall vertical - angle property

Vertical angles are congruent. When two lines intersect, the pairs of opposite angles formed are vertical angles.
In the figure, lines $AB$ and $CD$ intersect at point $O$. $\angle AOD$ and $\angle BOC$ are vertical angles.

Step2: Analyze other angle - pairs

$\angle AOB$ and $\angle AOD$ are adjacent angles that are not congruent (they are supplementary in this case). $\angle BOC$ and $\angle AOB$ are adjacent angles and not congruent. $\angle AOD$ and $\angle AOC$ are adjacent angles and not congruent.

Answer:

C. $\angle AOD$ and $\angle BOC$