Question

find the measure of \\( \angle orq \\).

\\( m \angle orq = \square ^ { \circ } \\)

Explanation:

Step1: Use the property of parallel lines

Since \(MN\parallel OP\), the angles \((9x - 4)^{\circ}\) and \((3x + 40)^{\circ}\) are same - side interior angles. And same - side interior angles are supplementary, so \((9x-4)+(3x + 40)=180\).

Step2: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

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

Substitute \(x = 12\) into \((3x + 40)^{\circ}\). Then \(3x+40=3\times12 + 40=36+40 = 76\)

Answer:

\(76\)