Question

16 lines q and s are parallel and cut by transversal r. if ∠2 = 28x - 10 and ∠7 = 26x + 6, then solve for x.

Explanation:

Step1: Use the property of alternate exterior angles

When two parallel lines are cut by a transversal, alternate exterior angles are equal. Here, \(\angle2\) and \(\angle7\) are alternate exterior angles. So, \(28x - 10=26x + 6\).

Step2: Solve the equation for \(x\)

Subtract \(26x\) from both sides: \(28x-26x - 10=26x-26x + 6\), which simplifies to \(2x-10 = 6\).
Add \(10\) to both sides: \(2x-10 + 10=6 + 10\), so \(2x=16\).
Divide both sides by \(2\): \(x=\frac{16}{2}\).

Answer:

\(x = 8\)