Question

if line m is parallel to line n, what is the value of x for the given picture?

Explanation:

Step1: Use the property of parallel lines

When two parallel lines are cut by a transversal, alternate - interior angles are equal. Here, \(3x + 15\) and \(75\) are alternate - interior angles. So, \(3x+15 = 75\).

Step2: Solve the equation for \(x\)

Subtract \(15\) from both sides of the equation:
\(3x+15−15=75 - 15\)
\(3x=60\)
Divide both sides by \(3\):
\(x=\frac{60}{3}\)

Answer:

\(x = 20\)