Question

solve for x.

x =

Explanation:

Step1: Find the supplementary angle

Since \( \angle JPN = 118^{\circ}\), its supplementary angle \( \angle MPO=180 - 118=62^{\circ}\) (linear - pair angles are supplementary).

Step2: Use the property of parallel lines

Because \( KL\parallel MN\) (given by the arrow - head marks), \(4x + 38=\angle MPO\) (corresponding angles are equal). So \(4x+38 = 62\).

Step3: Solve the equation for \(x\)

Subtract 38 from both sides: \(4x=62 - 38\), so \(4x = 24\).
Divide both sides by 4: \(x=\frac{24}{4}\).

Answer:

\(x = 6\)