Question

complete the paragraph proof.
we are given that $overrightarrow{eb}$ bisects $angle aec$. from the diagram, $angle ced$ is a right angle, which measures 90 degrees. since the measure of a straight angle is $180^circ$, the measure of angle aec must also be $90^circ$ by the dropdown options: angle addition postulate, reflexive property, segment addition property, symmetric property. a bisector cuts the angle measure in half.

Explanation:

Step1: Recall Angle Addition Postulate

The angle addition postulate states that if a point lies in the interior of an angle, the sum of the two smaller angles formed is equal to the measure of the larger angle. Here, since \( \angle AEC \) and \( \angle CED \) form a straight angle (sum to \( 180^\circ \)) and \( \angle CED = 90^\circ \), we use the angle addition postulate (\( m\angle AEC + m\angle CED = 180^\circ \)) to find \( m\angle AEC = 90^\circ \). Other properties (reflexive, segment addition, symmetric) don't apply here as they relate to congruence/equality of segments/angles in different contexts, not angle sum for a straight line.

Answer:

angle addition postulate