We are asked to find the measure of XZ which is expressed as 3x+5. To do so, we should first find the value of x. Let's consider the given diagram.
We can see that ∠ XWZ and ∠ YWZ have the same measure. Therefore, WZ is the bisector of ∠ XWY. From here, by the Angle Bisector Theorem, we can define the relationship between XZ and YZ.
Angle Bisector Theorem
If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.
According to the theorem, Z is equidistant from the sides of ∠ XWY. In other words, XZ and YZ have the same length. With this information, we can set the expressions for their lengths equal to one another.
3x+5=5x-7
Let's solve this equation for x.
