Question

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

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the given angles \((2x + 5)^{\circ}\) and \((9x+10)^{\circ}\) are alternate - exterior angles. Alternate - exterior angles are congruent when two parallel lines are cut by a transversal. So, \(2x + 5=9x+10\).

Step2: Solve the equation for \(x\)

First, subtract \(2x\) from both sides: \(5 = 9x+10 - 2x\), which simplifies to \(5=7x + 10\). Then subtract 10 from both sides: \(5-10=7x\), so \(- 5=7x\). Finally, divide both sides by 7: \(x=-\frac{5}{7}\).

Answer:

\(x =-\frac{5}{7}\)