Question

find the measure of \\( \angle f l i \\).

Explanation:

Step1: Use the property of alternate interior angles

Since \(HI\parallel JK\), \(\angle FLI=(7x - 13)^{\circ}\) and \(\angle GMK=(6x + 8)^{\circ}\) are alternate interior angles. So \(7x-13 = 6x + 8\).

Step2: Solve the equation for \(x\)

Subtract \(6x\) from both sides of the equation \(7x-13 = 6x + 8\):
\(7x-6x-13=6x-6x + 8\)
\(x-13=8\)
Add \(13\) to both sides: \(x=8 + 13=21\)

Step3: Calculate the measure of \(\angle FLI\)

Substitute \(x = 21\) into the expression for \(\angle FLI\):
\(\angle FLI=(7x-13)^{\circ}\)
\(=7\times21-13\)
\(=147-13\)
\(=134^{\circ}\)

Answer:

\(134\)