Question

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

Explanation:

Step1: Use the property of alternate interior angles

Since \( LM\parallel NO\), \( \angle MPQ=\angle NQP\) (alternate interior angles). And \( \angle NQP = 5x - 18\), \( \angle MPQ=4x + 12\). 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 \( \angle MPQ=4x + 12\). So \( \angle MPQ=4\times30+12=120 + 12=132\).

Answer:

\(132\)