Question

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

Explanation:

Step1: Use the property of alternate interior angles

Since \(HI\parallel JK\), \(\angle FLI=(147 - x)^{\circ}\) (alternate interior angles are equal). Also, \(\angle FLI=(5x - 3)^{\circ}\) (given). So, \(5x-3 = 147 - x\).

Step2: Solve the equation for \(x\)

Add \(x\) to both sides: \(5x+x-3=147 - x+x\), \(6x-3 = 147\).
Add \(3\) to both sides: \(6x-3 + 3=147+ 3\), \(6x=150\).
Divide both sides by \(6\): \(x=\frac{150}{6}=25\).

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

Substitute \(x = 25\) into \((5x - 3)^{\circ}\). \(5x-3=5\times25-3=125 - 3=122\).

Answer:

\(122\)