Question

solve for x.

x =

Explanation:

Step1: Use the property of consecutive interior angles

Since \(QR\parallel ST\), the consecutive interior angles \(\angle QUV\) and \(\angle SVU\) are supplementary. So, \(102^{\circ}+(10x - 2)^{\circ}=180^{\circ}\).

Step2: Simplify the equation

$$
LATEXBLOCK0
$$

Step3: Solve for \(x\)

Subtract \(100\) from both sides: \(10x=180 - 100\), so \(10x = 80\). Then divide both sides by \(10\): \(x=\frac{80}{10}=8\).

Answer:

\(8\)