Question

solve for x.

Explanation:

Step1: Use the property of same - side interior angles

When two parallel lines \(GH\) and \(IJ\) are cut by a transversal \(EF\), the sum of same - side interior angles \(\angle GKL\) and \(\angle ILK\) is \(180^{\circ}\). So, \((100 - 2x)+10x=180\).

Step2: Simplify the equation

Combine like terms: \(100+( - 2x + 10x)=180\), which gives \(100 + 8x=180\).
Subtract \(100\) from both sides: \(8x=180 - 100\), so \(8x=80\).

Step3: Solve for \(x\)

Divide both sides by \(8\): \(x=\frac{80}{8}\).

Answer:

\(x = 10\)