Question

two parallel lines are crossed by a transversal. what is the value of x? x = 12 x = 14 x = 22 x = 24

Explanation:

Step1: Use the property of parallel lines

When two parallel lines are crossed by a transversal, the consecutive interior angles are supplementary. So, \((5x + 5)+115=180\).

Step2: Simplify the equation

Simplify the left - hand side of the equation: \(5x+5 + 115=5x+120\). Then the equation becomes \(5x+120 = 180\).

Step3: Solve for \(x\)

Subtract 120 from both sides: \(5x=180 - 120\), so \(5x=60\). Divide both sides by 5: \(x=\frac{60}{5}=12\).

Answer:

\(x = 12\) (the first option)