Question

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

\\( m \angle m p q = \\) \\( \circ \\)

Explanation:

Step1: Use the property of parallel lines

Since \( LM\parallel NO\), then \(\angle MPQ+(4x + 30)^{\circ}=180^{\circ}\) (consecutive interior angles are supplementary). So \(9x-35+4x + 30=180\).

Step2: Solve the equation for \(x\)

Combine like terms: \(13x-5 = 180\).
Add \(5\) to both sides: \(13x=180 + 5=185\).
Divide both sides by \(13\): \(x = 15\).

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

Substitute \(x = 15\) into \(9x-35\).
\(9x-35=9\times15-35=135-35 = 100\).

Answer:

\(100\)