Question

in the figure below, \\( \overline { x z } \\) is a bisector of \\( \overline { y w } \\), \\( x z = 60 \mathrm { cm } \\), and \\( \overline { y w } = 250 \mathrm { cm } \\). what is the length of \\( \overline { e w } \\), in centimeters?
\\( \mathbf { a } \\) 100
\\( \mathbf { b } \\) 115
\\( \mathbf { c } \\) 125
\\( \mathbf { d } \\) 130

Explanation:

Step1: Recall the property of a bisector

Since \( \overline{XZ} \) is a bisector of \( \overline{YW} \), it divides \( \overline{YW} \) into two equal parts. But wait, no, actually, when two lines intersect, vertical angles are equal. But here, since \( \overline{XZ} \) bisects \( \overline{YW} \), \( YE = EW=\frac{YW}{2}\). Wait, no, hold on. Wait, actually, the problem might have a typo. Wait, no, if \( \overline{XZ} \) bisects \( \overline{YW} \), then \( YE = EW \). But we also have \( \angle YEX=\angle ZEW\) (vertical angles). But maybe the problem is using the fact that \( YE + EW=YW\). Since \( YE = EW\) (bisector), \( EW=\frac{YW}{2}\). But wait, no, wait the length of \( XZ \) is given. Wait, no, no—wait, no, the problem is: when two lines intersect (here \( YW \) and \( XZ \) intersect at \( E \)), and \( XZ \) bisects \( YW \), then \( YE = EW \). So \( EW=\frac{YW}{2}\). Given \( YW = 250\) cm.

Step2: Calculate \( EW \)

\( EW=\frac{YW}{2}=\frac{250}{2}=125\) cm.

Answer:

C. 125