Question

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

Explanation:

• First, note that \(\angle CEF+\angle FEG = 90^{\circ}\) (since \(\angle CEG = 90^{\circ}\) as it is a right - angle). So \(\angle FEG\) is the complement of \(\angle CEF\).
• The problem states that \(\angle CEF\) is complementary to \(\angle DCF\), which means \(\angle CEF+\angle DCF=90^{\circ}\).
• By the definition of complementary angles, if \(\angle A+\angle B = 90^{\circ}\) and \(\angle A+\angle C=90^{\circ}\), then \(\angle B=\angle C\). Here, \(\angle A=\angle CEF\), \(\angle B = \angle FEG\), and \(\angle C=\angle DCF\).

Answer:

Complements of the same angle are congruent.