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: Recall angle - related definitions

Complementary angles add up to 90°, and supplementary angles add up to 180°. Congruent angles have the same measure.

Step2: Analyze the given information

Since ∠FCD is a right - angle (90°), and ∠FCE≅∠ECD, then ∠FCE = ∠ECD=45°. Also, ∠ECD is complementary to ∠DCB, so ∠ECD + ∠DCB = 90°. Then ∠DCB = 45°. And ∠ACF=45°.

Step3: Check the relationship between ∠DCB and ∠ACF

∠DCB=45° and ∠ACF = 45°, so ∠DCB≅∠ACF. Also, ∠DCB+∠ACF=45° + 45°=90°, so they are complementary.

Answer:

They are congruent and complementary.