Question

parallel lines s and t are cut by a transversal, r, as shown. what is the value of x to the nearest whole number? 18 20 86 94

Explanation:

Step1: Find the measure of angle 1

Since \(s\parallel t\), angle \(1\) and the \(94^{\circ}\) angle are supplementary (consecutive interior angles). So, \(\angle1 = 180^{\circ}- 94^{\circ}=86^{\circ}\).

Step2: Set up the equation for \(x\)

We know that \(\angle1=(5x - 4)^{\circ}\). Substitute \(\angle1 = 86^{\circ}\) into the equation: \(5x-4=86\).

Step3: Solve the equation for \(x\)

Add \(4\) to both sides: \(5x=86 + 4\), so \(5x=90\).
Divide both sides by \(5\): \(x=\frac{90}{5}=18\).

Answer:

\(18\)