Question

complementary and supplementary angles
assignment active
justifying a statement
based on the diagram, which reason justifies this statement?
if $angle cef$ is complementary to $angle dcf$, then $angle dcf cong angle feg$.
$circ$ complements of the same angle are congruent.
$circ$ complements of congruent angles are congruent.
$circ$ supplements of the same angle are congruent.
$circ$ supplements of congruent angles are congruent.

Explanation:

First, identify that $\angle CEF$ and $\angle FEG$ are complementary, since $\angle CEG$ is a right angle (marked on the diagram), so $\angle CEF + \angle FEG = 90^\circ$. The problem states $\angle CEF$ is complementary to $\angle DCF$, meaning $\angle CEF + \angle DCF = 90^\circ$. Both $\angle DCF$ and $\angle FEG$ are complements of the same angle ($\angle CEF$), so they must be congruent by the rule that complements of the same angle are congruent.

Answer:

A. Complements of the same angle are congruent.