We are asked to find the measure of XY which, on the given diagram, is expressed as 6x-3. We are going to start by calculating x. Let's consider the given diagram.
From the diagram, we can see that ∠ ZWY and ∠ YWX have the same measure. Therefore, WY is the angle bisector of ∠ ZWX. Next, let's recall the Angle Bisector Theorem.
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 this theorem, Y is equidistant from the sides of ∠ ZWX. In other words, distances ZY and YX are the same. Let's set the expressions for their lengths equal to one another.
4x+5=6x-3
Now we have an equation where the only unknown variable is x. Let's solve it to find the value of x.
