Question

1. which value of x will show that line m is parallel to line r? a) 25 b) 24 c) 33 d) 20

Explanation:

Step1: Use the property of parallel lines (alternate - exterior angles)

When two parallel lines are cut by a transversal, alternate - exterior angles are equal. So, if \(r\parallel m\), then \(7x - 115=3x - 35\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides of the equation:
\(7x-3x - 115=3x-3x - 35\)
\(4x-115=- 35\)
Add \(115\) to both sides:
\(4x-115 + 115=-35 + 115\)
\(4x=80\)
Divide both sides by \(4\):
\(x = 20\)

Answer:

d) \(20\)