Question

Ray CE is the angle bisector of ACD. Which statement about the figure must be true?

Answer 1

we know that

"Bisect" means to divide into two equal parts

so

If the ray CE is the angle bisector of ADC

then

$Angle(ACD)=Angle(ACE)+Angle(ECD)$

$Angle(ACE)=Angle(ECD)$

so

$Angle(ACD)=2Angle(ACE)$

$Angle(ACE)=\frac{1}{2} Angle(ACD)$

therefore

the answer is the option

$Angle(ACE)=\frac{1}{2} Angle(ACD)$

or

$Angle(ACE)=Angle(ECD)$

Answer 2

This is the concept of algebra, given that Ray CE is bisector of ACD, this implies that the ray has divided ACD equally hence, mACE=mECD. 
Also mACE=mDCB. The reason being they are all corresponding angles.