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 explain why the angles from the previous step are congruent angles. choose the correct answer below. a. they are complements of the same angle. b. they are supplementary angles. c. they are supplements of the same angle. d. they are complementary angles.

Explanation:

Step1: Identify vertical - angle property

When two lines intersect, vertical angles are congruent. In the given figure, $\angle AOD$ and $\angle BOC$ are vertical angles, and $\angle AOB$ and $\angle DOC$ are also vertical angles.

Step2: Recall the definition of vertical angles

Vertical angles are formed by two intersecting lines. $\angle AOD$ and $\angle BOC$ are formed by the intersection of lines $AB$ and $CD$ at point $O$. Complementary angles add up to $90^{\circ}$ and supplementary angles add up to $180^{\circ}$. Vertical angles are supplements of the same angle. For example, $\angle AOD+\angle AOC = 180^{\circ}$ and $\angle BOC+\angle AOC=180^{\circ}$. So, $\angle AOD$ and $\angle BOC$ are congruent because they are supplements of the same angle $\angle AOC$.

Answer:

Name one pair of congruent angles: C. $\angle AOD$ and $\angle BOC$
Explain why the angles from the previous step are congruent angles: C. They are supplements of the same angle.