given: $ \overrightarrow{ad} $.
$ \overrightarrow{eb} $ bisects $ \angle aec $
what statements are true regarding the given
statement and diagram?
$ \square \angle ced $ is a right angle.
$ \square \angle cea $ is a right angle.
$ \square m \angle cea=\frac{1}{2}(m \angle ceb) $
$ \square m \angle ceb=m \angle bea $
$ \square m \angle deb = 135^{\circ} $
$ \square m \angle aeb = 35^{\circ} $

Question

Accepted Answer

# Explanation:
## Step1: Analyze $\angle CED$
Since $EC\perp ED$ (right - angle symbol at $E$ between $EC$ and $ED$), by the definition of a right - angle ($90^{\circ}$ angle), $\angle CED = 90^{\circ}$, so $\angle CED$ is a right angle.
## Step2: Analyze $\angle CEA$
$\angle CEA$ is not a right angle. A right angle is $90^{\circ}$, and $\angle CEA=\angle CEB+\angle BEA$.
## Step3: Analyze $m\angle CEA=\frac{1}{2}(m\angle CEB)$
Since $\overrightarrow{EB}$ bisects $\angle AEC$, by the angle - bisector definition $m\angle CEB = m\angle BEA$ and $m\angle CEA=m\angle CEB + m\angle BEA=2m\angle CEB$, so $m\angle CEA=\frac{1}{2}(m\angle CEB)$ is false.
## Step4: Analyze $m\angle CEB=m\angle BEA$
Because $\overrightarrow{EB}$ bisects $\angle AEC$, by the angle - bisector definition (a ray that divides an angle into two congruent adjacent angles), $m\angle CEB = m\angle BEA$.
## Step5: Analyze $m\angle DEB$
Since $\angle CED = 90^{\circ}$ and $\angle CEB=\angle BEA$, and $\angle AEC+\angle CED = 180^{\circ}$ (linear pair), $\angle AEC = 90^{\circ}$, then $\angle CEB=\angle BEA = 45^{\circ}$. Using the linear - pair relationship $\angle DEB=\angle DEC+\angle CEB$, and since $\angle DEC = 90^{\circ}$ and $\angle CEB = 45^{\circ}$, $m\angle DEB=90^{\circ}+45^{\circ}=135^{\circ}$.
## Step6: Analyze $m\angle AEB$
Since $\angle AEC = 90^{\circ}$ and $\overrightarrow{EB}$ bisects $\angle AEC$, $m\angle AEB=\frac{1}{2}m\angle AEC = 45^{\circ}
eq35^{\circ}$

# Answer:
$\angle CED$ is a right angle, $m\angle CEB = m\angle BEA$, $m\angle DEB = 135^{\circ}$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Analyze \(\angle CED\)

Step2: Analyze \(\angle CEA\)

Step3: Analyze \(m\angle CEA=\frac{1}{2}(m\angle CEB)\)

Step4: Analyze \(m\angle CEB=m\angle BEA\)

Step5: Analyze \(m\angle DEB\)

Step6: Analyze \(m\angle AEB\)

Answer: