Question

ray ce is the angle bisector of ∠acd. which statement about the figure must be true?
○ m∠ecd = 1/2m∠ecb
○ m∠ace = 1/2m∠acd
○ ∠ace ≅ ∠dcb
○ ∠ecd ≅ ∠acd

Explanation:

Step1: Recall angle - bisector definition

An angle bisector divides an angle into two equal - measure angles.
Since ray CE is the angle bisector of ∠ACD, by the definition of an angle bisector, m∠ACE=m∠ECD and m∠ACE + m∠ECD=m∠ACD. So, m∠ACE=\frac{1}{2}m∠ACD and m∠ECD=\frac{1}{2}m∠ACD.

Answer:

m∠ACE=\frac{1}{2}m∠ACD