Question

which value of x will show that line m is parallel to line r? image: two parallel lines (m, r) cut by a transversal, with angles labeled ((7x - 115)^circ) and ((3x - 35)^circ). options: 24, 20, 25, 33

Explanation:

Step1: Identify the angle relationship

When two lines are parallel, the alternate exterior angles are equal. So, we set the two angle expressions equal: \(7x - 115 = 3x - 35\).

Step2: Solve for x

Subtract \(3x\) from both sides: \(7x - 3x - 115 = -35\) → \(4x - 115 = -35\).
Add 115 to both sides: \(4x = -35 + 115\) → \(4x = 80\).
Divide by 4: \(x = \frac{80}{4}\) → \(x = 20\).

Answer:

20