Question

solve for x.

x =

Explanation:

Step1: Use the property of same - side interior angles

When two parallel lines \(MN\) and \(OP\) are cut by a transversal \(KL\), the same - side interior angles \(\angle NQR=(5x - 32)^{\circ}\) and \(\angle QRP=(3x - 4)^{\circ}\) are supplementary. So, \((5x-32)+(3x - 4)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(5x+3x-32 - 4=180\), which gives \(8x-36 = 180\).

Step3: Isolate the term with \(x\)

Add \(36\) to both sides of the equation: \(8x-36+36=180 + 36\), so \(8x=216\).

Step4: Solve for \(x\)

Divide both sides by \(8\): \(x=\frac{216}{8}=27\).

Answer:

\(27\)