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

Question

Accepted Answer

# Explanation:
## Step1: Analyze $ m\angle CEA = 90^\circ $
From the diagram, $ \angle CEA $ is a right angle (marked with a square), so $ m\angle CEA = 90^\circ $. This statement is true.
## Step2: Analyze $ m\angle CEF = m\angle CEA + m\angle BEF $
Looking at the angles, $ \angle CEF $ is composed of $ \angle CEA $ and $ \angle AEF $, not $ \angle BEF $. So this statement is false.
## Step3: Analyze $ m\angle CEB = 2(m\angle CEA) $
Since $ \overrightarrow{EB} $ bisects $ \angle CEA $, $ \angle CEB=\angle BEA $. And $ \angle CEA = 90^\circ $, so $ \angle CEB = 45^\circ $, and $ 2(m\angle CEA)=180^\circ
eq45^\circ $. This statement is false.
## Step4: Analyze $ \angle CEF $ is a straight angle
Points $ C $, $ E $, $ F $ are colinear (since $ CF $ is a straight line), so $ \angle CEF = 180^\circ $, which is a straight angle. This statement is true.
## Step5: Analyze $ \angle AEF $ is a right angle
$ \angle CEA = 90^\circ $ and $ \angle CEF = 180^\circ $, so $ \angle AEF=\angle CEF-\angle CEA = 180^\circ - 90^\circ=90^\circ $, so $ \angle AEF $ is a right angle. This statement is true.

# Answer:
The three true statements are:
- $ m\angle CEA = 90^\circ $
- $ \angle CEF $ is a straight angle
- $ \angle AEF $ is a right angle

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QUESTION IMAGE

Question

Explanation:

Step1: Analyze \( m\angle CEA = 90^\circ \)

Step2: Analyze \( m\angle CEF = m\angle CEA + m\angle BEF \)

Step3: Analyze \( m\angle CEB = 2(m\angle CEA) \)

Step4: Analyze \( \angle CEF \) is a straight angle

Step5: Analyze \( \angle AEF \) is a right angle

Answer: