Question

find the measure of ∠loi.
m∠loi = □°

Explanation:

Step1: Use the property of corresponding angles

Since \(KJ\parallel ML\), \(\angle KNH=(5x + 19)^{\circ}\) and \(\angle LOI=(9x - 5)^{\circ}\) are corresponding angles. Corresponding angles are equal. 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 \(9x-5\).
\(9x-5=9\times6 - 5=54 - 5=49\).

Answer:

\(49\)