Question

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

mECD = mECB
mACE = mACD
ACE DCB
ECD ACD

Answer 1

ACE DCB

hope this helped

Answer 2

We are given that ray CE is an angle bisector of angle ACD. With this, we have the equation,
mACE = mECD

Next, we look at the choices
mECD = mECB > This not possible since ray CD is between the two angles
mACE = mACD > This is still not possible since ray CE is between the two angles
mACE = mDCB > This is possible since angles ACE, ECD and DCB are complementary angles.
mECD = mACD > This is not possible since ray CE is between the two rays

The answer is the third option