Question

find the value of x.

Explanation:

Step1: Apply the Angle - Bisector Theorem

The Angle - Bisector Theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the adjacent sides.
In \(\triangle XWZ\) with \(WY\) as the angle - bisector of \(\angle XWZ\), we have the proportion \(\frac{XY}{YZ}=\frac{WX}{WZ}\).
Given \(XY = 21\), \(YZ=30\), \(WX = 35\), and \(WZ=x + 0\) (where \(WZ\) is composed of two segments, and we need to find \(x\)).
The proportion becomes \(\frac{21}{30}=\frac{35}{x}\).

Step2: Cross - multiply to solve for \(x\)

Cross - multiplying gives \(21x=30\times35\).
First, calculate \(30\times35 = 1050\). So, \(21x = 1050\).
Then, divide both sides by 21: \(x=\frac{1050}{21}\).
Since \(1050\div21 = 50\).

Answer:

\(50\)