Question

given: (overrightarrow{eb}) bisects (angle aec). (angle aed) is a straight angle. prove: (mangle aeb = 45^{circ}) complete the paragraph proof. we are given that (overrightarrow{eb}) bisects (angle aec). from the diagram, (angle ced) is a right angle, which measures degrees. since the measure of a straight angle is (180^{circ}), the measure of angle must also be (90^{circ}) by the. a bisector cuts the angle measure in half. (mangle aeb) is (45^{circ}).

Explanation:

Step1: Recall right - angle measure

A right - angle measures 90 degrees. So, since $\angle CED$ is a right angle, it measures 90 degrees.

Step2: Use straight - angle property

$\angle AED$ is a straight angle and measures 180 degrees. $\angle AED=\angle AEC+\angle CED$. Since $\angle CED = 90^{\circ}$, then $\angle AEC=180^{\circ}-\angle CED=180 - 90=90^{\circ}$ by the angle - addition postulate.

Step3: Apply angle - bisector definition

$\overrightarrow{EB}$ bisects $\angle AEC$. By the definition of an angle bisector, it divides $\angle AEC$ into two equal angles. So, $m\angle AEB=\frac{1}{2}m\angle AEC$. Since $m\angle AEC = 90^{\circ}$, then $m\angle AEB=\frac{90^{\circ}}{2}=45^{\circ}$.

Answer:

The blanks should be filled as follows: 90; $\angle AEC$; angle - addition postulate.