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

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

Answer 2

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
`\\eq` m∠CEA + m∠BEF

case 3) m∠CEB = 2(m∠CEA)

Is False

m∠CEB=
`45`°

2(m∠CEA)=
`2*90=180`°

m∠CEB
`\\eq` 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