Question

given m||n, find the value of x.

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the two given angles \((9x + 10)^{\circ}\) and \((8x-14)^{\circ}\) are alternate - interior angles. Alternate - interior angles formed by two parallel lines and a transversal are congruent. So, \(9x + 10=8x - 14\).

Step2: Solve the equation for \(x\)

Subtract \(8x\) from both sides of the equation: \(9x-8x + 10=8x-8x - 14\), which simplifies to \(x+10=-14\).
Then subtract 10 from both sides: \(x+10 - 10=-14 - 10\).
So, \(x=-24\).

Answer:

\(x=-24\)