Question

find the measure of \\( \angle m p q \\).

Explanation:

Step1: Use the property of parallel lines

Since \( LM\parallel NO\), the angles \((4x + 12)^{\circ}\) and \((5x-18)^{\circ}\) are equal (alternate interior angles). So, \(4x + 12=5x - 18\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(12=x - 18\). Then add \(18\) to both sides: \(x=12 + 18=30\).

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

Substitute \(x = 30\) into \(4x+12\). We get \(4\times30+12=120 + 12=132\).

Answer:

\(132\)