Question

justifying a statement. based on the diagram, which reason justifies this statement? if ∠cef is complementary to ∠dcf, then ∠dcf ≅ ∠feg. supplements of congruent angles are congruent. complements of congruent angles are congruent. complements of the same angle are congruent. supplements of the same angle are congruent.

Explanation:

We know that $\angle CEF$ and $\angle FEG$ are complementary (since $\angle CEG = 90^{\circ}$). Given that $\angle CEF$ is complementary to $\angle DCF$, both $\angle DCF$ and $\angle FEG$ are complements of $\angle CEF$. By the property that complements of the same angle are congruent, we can justify the statement.

Answer:

Complements of the same angle are congruent.