Question

given l || m || n, find the value of x. (5x + 15)° (6x + 8)°

Explanation:

Step1: Use property of parallel lines

Since \(l\parallel m\parallel n\), the angles \((5x + 15)^{\circ}\) and \((6x+8)^{\circ}\) are equal (corresponding - angles or alternate - interior angles depending on the transversal, and for parallel lines, such non - adjacent angles formed by a transversal are equal). So we set up the equation \(5x + 15=6x + 8\).

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides of the equation: \(5x+15-5x=6x + 8-5x\), which simplifies to \(15=x + 8\). Then subtract 8 from both sides: \(15 - 8=x+8 - 8\), so \(x = 7\).

Answer:

\(x = 7\)