Question

in the figure, line q is parallel to line r, and both lines are intersected by line s. if y = 2x + 9, what is the value of x? a. 11 b. 20 c. 70 d. 80 note: figure not drawn to scale

Explanation:

Step1: Use the property of parallel lines

When two parallel lines (q and r) are intersected by a transversal (s), corresponding - angles or alternate - interior/exterior angles are equal. Assume that the angle related to \(y\) and the \(31^{\circ}\) angle are supplementary (linear - pair or related by parallel - line properties). So \(y + 31^{\circ}=180^{\circ}\), then \(y = 180 - 31=149^{\circ}\).

Step2: Substitute \(y\) into the equation

We know that \(y = 2x + 9\). Substitute \(y = 149\) into the equation: \(149=2x + 9\).

Step3: Solve for \(x\)

First, subtract 9 from both sides of the equation: \(149−9 = 2x+9 - 9\), which gives \(140 = 2x\). Then divide both sides by 2: \(x=\frac{140}{2}=70\).

Answer:

c. 70