Question

1. given the parallel lines cut by a transversal, find the value of x:

a. 60
b. 12
c. 17
d. 64

Explanation:

Step1: Use the property of supplementary angles

When two parallel lines are cut by a transversal, consecutive - interior angles are supplementary. So, \(61^{\circ}+(7x)^{\circ}=180^{\circ}\).

Step2: Solve the equation for \(x\)

Subtract \(61\) from both sides of the equation: \(7x = 180 - 61\). Then \(7x=119\). Divide both sides by \(7\): \(x=\frac{119}{7}\).

Answer:

\(x = 17\), so the answer is C.