Question

right angle fcd intersects ab and ce at point c. ∠fce is congruent to ∠ecd. ∠ecd is complementary to ∠dcb. which statement is true about ∠dcb and ∠acf? they are congruent and complementary. they are congruent and supplementary. they are complementary but not necessarily congruent. they are supplementary but not necessarily congruent.

Explanation:

Step1: Analyze given angle - relationships

Given $\angle FCD = 90^{\circ}$ and $\angle FCE\cong\angle ECD$, so $\angle FCE=\angle ECD = 45^{\circ}$. Also, $\angle ECD$ is complementary to $\angle DCB$, so $\angle ECD+\angle DCB = 90^{\circ}$, then $\angle DCB=45^{\circ}$. And $\angle ACF = 45^{\circ}$.

Step2: Check congruence and complement - supplement properties

Since $\angle DCB = 45^{\circ}$ and $\angle ACF = 45^{\circ}$, they are congruent. Also, $\angle DCB+\angle ACF=45^{\circ}+45^{\circ}=90^{\circ}$, so they are complementary.

Answer:

They are congruent and complementary.