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
