Question

use the figure below to answer the following question: if $overrightarrow{yw}$ is the angle bisector of $mangle vyx$, which of the following conclusions could be made? $mangle vyw = mangle xyw$ $overrightarrow{yw}$ is the angle bisector of $mangle vyw$ $angle xywcongangle xyv$ $overrightarrow{yx}$ is the angle bisector of $mangle vyx$

Explanation:

Step1: Recall angle - bisector definition

An angle bisector divides an angle into two congruent angles. If $\overrightarrow{YW}$ is the angle bisector of $\angle VYX$, then $\angle VYW$ and $\angle XYW$ are the two congruent angles formed.

Step2: Analyze each option

• For the option $m\angle VYW = m\angle XYW$, by the definition of an angle - bisector, when $\overrightarrow{YW}$ bisects $\angle VYX$, it divides $\angle VYX$ into two equal - measure angles $\angle VYW$ and $\angle XYW$.
• The option $\overrightarrow{YW}$ is the angle bisector of $m\angle VYW$ is incorrect because $\overrightarrow{YW}$ is given as the bisector of $\angle VYX$, not $\angle VYW$.
• The option $\angle XYW\cong\angle XYV$ is incorrect. $\angle XYW$ and $\angle XYV$ are not the two equal parts formed by the bisector of $\angle VYX$.
• The option $\overrightarrow{YX}$ is the angle bisector of $m\angle VYX$ is incorrect since $\overrightarrow{YW}$ is the given angle bisector of $\angle VYX$.

Answer:

$m\angle VYW = m\angle XYW$