Question

find the measure of (angle loi).

(mangle loi=square^{circ})

Explanation:

Step1: Use the property of alternate exterior angles

Since \(KJ\parallel ML\), \(\angle KNO=\angle LOI\) (alternate exterior angles). And \(\angle KNO=(5x + 19)^{\circ}\), \(\angle LOI=(9x-5)^{\circ}\). So \(5x + 19=9x-5\).

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides: \(19 = 4x-5\).
Add \(5\) to both sides: \(24=4x\).
Divide both sides by \(4\): \(x = 6\).

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

Substitute \(x = 6\) into \(\angle LOI=(9x - 5)^{\circ}\).
\(\angle LOI=(9\times6-5)^{\circ}=(54 - 5)^{\circ}=49^{\circ}\).

Answer:

\(49\)