Question

find the value of y.
y = \square

Explanation:

Step1: Use the Angle Bisector Theorem

Since \(LK = LF\) (marked as equal) and \(LH\) is a common side, and \(\angle LKH=\angle LFH = 90^{\circ}\), by the Hypotenuse - Leg (HL) congruence criterion, \(\triangle LKH\cong\triangle LFH\). Then, by the Angle Bisector Theorem, \(8y=6y + 8\).

Step2: Solve the equation

Subtract \(6y\) from both sides of the equation \(8y=6y + 8\).
\(8y-6y=6y + 8-6y\)
\(2y=8\)
Divide both sides by 2: \(y=\frac{8}{2}\)

Answer:

\(y = 4\)