Question

A vertical line has points C, E, F from top to bottom. 2 lines extend from point E. One line extends to point A and another extends to point B. Angle A E C is 90 degrees.


Given that Ray E B bisects ∠CEA, which statements must be true? Select three options.

m∠CEA = 90°
m∠CEF = m∠CEA + m∠BEF
m∠CEB = 2(m∠CEA)
∠CEF is a straight angle.
∠AEF is a right angle.

Answer 1

Selected (true):
- m∠CEA = 90° (given)
- ∠CEF is a straight angle. (C, E, F are collinear, so CE and EF are opposite rays → 180°)
- ∠AEF is a right angle. (CE and EF are opposite rays so ∠AEF = 180° − ∠CEA = 180° − 90° = 90°)

False:
- m∠CEF = m∠CEA + m∠BEF (would give 180° = 90° + 135° if EB bisects ∠CEA → false)
- m∠CEB = 2(m∠CEA) (CEB = 45° while CEA = 90°, so CEB is half, not double)