Question

given ( mparallel n ), find the value of ( x ).

Explanation:

Step1: Use the property of alternate interior angles

Since \(m\parallel n\), the angles \((9x - 10)^{\circ}\) and \((8x+14)^{\circ}\) are alternate interior angles. Alternate interior angles are equal. 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 add \(10\) to both sides: \(x-10 + 10=14 + 10\).

Answer:

\(x = 24\)