Question

given that e 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.

Explanation:

Step1: Recall angle - bisector definition

If a ray bisects an angle, it divides the angle into two equal - sized angles. But we have no information to say \(m\angle CEA = 90^{\circ}\).

Step2: Analyze angle - sum relationship

\(m\angle CEF=m\angle CEA + m\angle AEF\), not \(m\angle CEF=m\angle CEA + m\angle BEF\).

Step3: Analyze angle - bisector relationship

If \(EB\) bisects \(\angle CEA\), then \(m\angle CEA = 2m\angle CEB\), not \(m\angle CEB = 2m\angle CEA\).

Step4: Identify straight - angle

Since points \(C\), \(E\), and \(F\) are collinear, \(\angle CEF\) is a straight angle by the definition of a straight angle (an angle whose measure is \(180^{\circ}\)).

Step5: Identify right - angle

Since \(EA\perp EF\) (as indicated by the right - angle symbol at \(\angle AEF\)), \(\angle AEF\) is a right angle.

Answer:

\(\angle CEF\) is a straight angle, \(\angle AEF\) is a right angle.