Question

solve for x.
x =

Explanation:

Step1: Find the measure of the angle adjacent to \(118^{\circ}\)

Since the sum of adjacent angles on a straight line is \(180^{\circ}\), the adjacent angle to \(118^{\circ}\) is \(180 - 118=62^{\circ}\)

Step2: Set up the equation using the property of parallel lines

Because \(KL\parallel MN\) (marked with red arrows), the angle \((4x + 38)^{\circ}\) and the \(62^{\circ}\) angle (found in Step 1) are equal (corresponding angles). So we have the equation \(4x+38 = 62\)

Step3: Solve the equation for \(x\)

Subtract \(38\) from both sides: \(4x=62 - 38\), so \(4x = 24\). Then divide both sides by \(4\): \(x=\frac{24}{4}=6\)

Answer:

\(6\)