Question

solve for x.

x =

Explanation:

Step1: Use the property of consecutive interior angles

Since lines \(QR\) and \(ST\) are parallel, and \(OP\) is a transversal, the consecutive interior angles \((102^{\circ})\) and \((10x - 2)^{\circ}\) are supplementary. So, \(102+(10x - 2)=180\).

Step2: Simplify the equation

Simplify the left - hand side of the equation: \(102 + 10x-2=10x + 100\). So the equation becomes \(10x+100 = 180\).

Step3: Solve for \(x\)

Subtract \(100\) from both sides: \(10x=180 - 100\), \(10x=80\). Then divide both sides by \(10\): \(x=\frac{80}{10}\).

Answer:

\(x = 8\)