Question

find the measure of ∠flj.
m∠flj=□°

Explanation:

Step1: Use the property of corresponding angles

Since \(GH\parallel IJ\), \(\angle GKL\) and \(\angle ILJ\) are corresponding angles. So \(8x - 12=5x + 18\).

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides: \(8x-5x - 12=5x-5x + 18\), which gives \(3x-12 = 18\).
Add \(12\) to both sides: \(3x-12 + 12=18 + 12\), so \(3x=30\).
Divide both sides by \(3\): \(x = 10\).

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

\(\angle FLJ\) and \((5x + 18)^{\circ}\) are supplementary (linear - pair).
First, find \(5x+18\) when \(x = 10\): \(5\times10+18=50 + 18=68^{\circ}\).
Since \(\angle FLJ+(5x + 18)^{\circ}=180^{\circ}\), then \(\angle FLJ=180-(5x + 18)\).
Substitute \(x = 10\): \(\angle FLJ=180 - 68=112^{\circ}\).

Answer:

\(112\)