Question

period: 7 november 10, 2025 6 in the diagram below, line p intersects line m and line n. if m∠1 = 7x and m∠2 = 5x + 30, lines m and n are parallel when x equals ① 12.5 ② 15 ③ 87.5 ④ 105

Explanation:

Step1: Use the property of parallel lines

When lines \(m\) and \(n\) are parallel, \(\angle1\) and \(\angle2\) are congruent (alternate - interior angles). So, \(7x=5x + 30\).

Step2: Solve the equation

Subtract \(5x\) from both sides: \(7x-5x=5x + 30-5x\), which gives \(2x=30\).
Divide both sides by \(2\): \(x=\frac{30}{2}=15\).

Answer:

1. \(15\)