Question

Given: ,

bisects ∠AEC.

A horizontal line has points A, E, D. 2 lines extend from point E. One line extends to point B and another extends to point C. A small box represents the angle for C E D.

What statements are true regarding the given statement and diagram?

∠CED is a right angle.
∠CEA is a right angle.
m∠CEA = One-half(m∠CEB)
m∠CEB = m∠BEA
m∠DEB = 135°
m∠AEB = 35°

Answer 1

True statements:
- ∠CED is a right angle. (The small box marks ∠CED = 90°.)
- ∠CEA is a right angle. (A, E, D are collinear so ∠CEA + ∠CED = 180°; since ∠CED = 90°, ∠CEA = 90°.)
- m∠CEB = m∠BEA. (EB bisects ∠AEC, so it splits the 90° angle into two equal parts.)
- m∠DEB = 135°. (With ∠CEA = 90° and EB bisecting it, each half is 45°. ED is opposite EA, so the angle from ED to EB is 180° − 45° = 135°.)

False statements:
- m∠CEA = 1/2(m∠CEB). (Actually m∠CEB = 1/2 m∠CEA, not the other way around.)
- m∠AEB = 35°. (m∠AEB = 45°, since EB makes a 45° angle with EA.)