Question

given that (overrightarrow{eb}) bisects (angle cea), which statements must be true? select three options.(mangle cea = 90^{circ})(mangle cef=mangle cea + mangle bef)(mangle ceb = 2(mangle cea))(angle cef) is a straight angle.(angle aef) is a right angle.

Explanation:

Step1: Recall angle - bisector and angle - relationship definitions

An angle - bisector divides an angle into two equal parts. A straight angle measures 180°, and a right angle measures 90°.

Step2: Analyze each option

• Option 1: Just because $\overrightarrow{EB}$ bisects $\angle CEA$, we have no information to say $m\angle CEA = 90^{\circ}$.
• Option 2: $m\angle CEF=m\angle CEA + m\angle AEF$, not $m\angle CEA + m\angle BEF$.
• Option 3: Since $\overrightarrow{EB}$ bisects $\angle CEA$, $m\angle CEB=\frac{1}{2}(m\angle CEA)$, not $m\angle CEB = 2(m\angle CEA)$.
• Option 4: $\angle CEF$ is a straight angle because points $C$, $E$, and $F$ are collinear. By the definition of a straight - angle (an angle whose measure is 180°), $\angle CEF$ is a straight angle.
• Option 5: Since $\angle AEF$ is formed by two perpendicular - looking lines (from 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.