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=[tex] 90 [/tex]°
m∠AEB=m∠BEC=[tex] 45 [/tex]°
Statements
case 1) m∠CEA=[tex] 90 [/tex]°
Is True
∠CEA is a right angle
case 2) m∠CEF = m∠CEA + m∠BEF
Is False
we know that
m∠CEF=[tex] 180 [/tex]° ---> is a straight angle
and
m∠CEA + m∠BEF=[tex] 90+135=225 [/tex]°
m∠CEF [tex] \neq [/tex] m∠CEA + m∠BEF
case 3) m∠CEB = 2(m∠CEA)
Is False
m∠CEB=[tex] 45 [/tex]°
2(m∠CEA)=[tex] 2*90=180 [/tex]°
m∠CEB [tex] \neq [/tex] 2(m∠CEA)
case 4) m∠BEF = 135°
Is True
m∠BEF=m∠BEA+m∠AEF
m∠BEA=[tex] 45 [/tex]°
m∠AEF=[tex] 90 [/tex]°
Substitute
m∠BEF=[tex] 45+90=135 [/tex]°
case 5) ∠CEF is a straight angle
Is True
m∠CEF=[tex] 180 [/tex]°
case 6) ∠AEF is a right angle
Is True
m∠AEF=[tex] 90 [/tex]°
therefore
the answers are
m∠CEA=[tex] 90 [/tex]°
m∠BEF = 135°
∠CEF is a straight angle
∠AEF is a right angle
