Question

Given that bisects ∠CEA, which statements must be true? Check all that apply. m∠CEA = 90° m∠CEF = m∠CEA + m∠BEF m∠CEB = 2(m∠CEA) m∠BEF = 135° ∠CEF is a straight angle. ∠AEF is a right angle.

Answer 1

see the attached figure to better understand the problem

we know that

An angle bisector divides the angle into two angles with equal measures

So

m∠CEA=$90$°

m∠AEB=m∠BEC=$45$°

Statements

case 1) m∠CEA=$90$°

Is True

∠CEA is a right angle

case 2) m∠CEF = m∠CEA + m∠BEF

Is False

we know that

m∠CEF=$180$° ---> is a straight angle

and

m∠CEA + m∠BEF=$90+135=225$°

m∠CEF $\neq$ m∠CEA + m∠BEF

case 3) m∠CEB = 2(m∠CEA)

Is False

m∠CEB=$45$°

2(m∠CEA)=$2*90=180$°

m∠CEB $\neq$ 2(m∠CEA)

case 4) m∠BEF = 135°

Is True

m∠BEF=m∠BEA+m∠AEF

m∠BEA=$45$°

m∠AEF=$90$°

Substitute

m∠BEF=$45+90=135$°

case 5) ∠CEF is a straight angle

Is True

m∠CEF=$180$°

case 6) ∠AEF is a right angle

Is True

m∠AEF=$90$°

therefore

the answers are

m∠CEA=$90$°

m∠BEF = 135°

∠CEF is a straight angle

∠AEF is a right angle

Answer 2

The 1,3,4
that is what i think it might be but i could be wrong