Question

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

Explanation:

Step1: Identify vertical - angle property

Vertical angles are congruent. In the given figure, when two lines intersect, vertical angles are formed.

Step2: Find first pair of congruent angles

$\angle AOD$ and $\angle BOC$ are vertical angles, also $\angle AOC$ and $\angle BOD$ are vertical angles. But considering the options, $\angle AOD$ and $\angle BOC$ are not given. For the pair in the option, $\angle AOD$ and $\angle AOC$ are supplementary to $\angle DOC$. If $\angle DOC=\alpha$, $\angle AOD = 180^{\circ}-\alpha$ and $\angle AOC = 180^{\circ}-\alpha$, so they are supplements of the same angle.

Step3: Find second pair of congruent angles

$\angle AOB$ and $\angle COD$ are vertical angles. Vertical angles are equal in measure, so they are congruent.

Answer:

First - pair: D. $\angle AOD$ and $\angle AOC$; Reason: C. They are supplements of the same angle.
Second - pair: A. $\angle AOB$ and $\angle COD$