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 property of parallel lines and transversal

When two parallel lines are cut by a transversal, the sum of an interior angle and its corresponding exterior - like angle (in this case, the \(120^{\circ}\) angle and \((5x)^{\circ}\) angle are supplementary). So, \(120 + 5x=180\).

Step2: Solve the equation for \(x\)

Subtract \(120\) from both sides of the equation:
\(5x=180 - 120\)
\(5x = 60\)
Divide both sides by \(5\): \(x=\frac{60}{5}=12\)

Answer:

B. 12