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. ∠afb and ∠cfd b. ∠bfc and ∠dfe c. ∠efd and ∠afb d. ∠cfd and ∠afe explain why the angles from the previous step are congruent angles. choose the correct answer below. a. they are right angles and all right angles are congruent. b. they are supplements of the same angle. c. they are vertical angles. d. they are complements of the same angle.

Explanation:

First Sub - Question (Name one pair of congruent angles)

To determine the congruent angles, we analyze the figure. $\angle BFC$ and $\angle DFE$ are both right angles (as indicated by the right - angle symbol in the figure). All right angles have a measure of $90^{\circ}$, so they are congruent. Let's check the other options:

• Option A: $\angle AFB$ and $\angle CFD$ do not have the same measure (from the figure's right - angle markings and angle relationships).
• Option C: $\angle EFD$ and $\angle AFB$ do not have the same measure.
• Option D: $\angle CFD$ and $\angle AFE$ do not have the same measure.

So the correct pair is $\angle BFC$ and $\angle DFE$.

$\angle BFC$ and $\angle DFE$ are both right angles. By the definition of a right angle, each has a measure of $90^{\circ}$. Since all angles with a measure of $90^{\circ}$ are congruent, the reason they are congruent is that they are right angles and all right angles are congruent. Let's analyze the other options:

• Option B: They are not supplements of the same angle. Supplements add up to $180^{\circ}$, and these are right angles (add up to $90^{\circ}$).
• Option C: Vertical angles are formed by two intersecting lines and are opposite each other. These are not vertical angles.
• Option D: Complements add up to $90^{\circ}$, and these angles are already $90^{\circ}$, so they are not complements of the same angle.

Answer:

B. $\angle BFC$ and $\angle DFE$

Second Sub - Question (Explain why the angles are congruent)