Question

given m||n, find the value of x. answer attempt 1 out of 2 x =

Explanation:

Step1: Use property of parallel lines

When two parallel lines are cut by a transversal, corresponding - angles are equal. Here, the angles \((5x - 10)^{\circ}\) and \((6x + 3)^{\circ}\) are supplementary (because they are same - side interior angles, and for parallel lines \(m\parallel n\), same - side interior angles add up to \(180^{\circ}\)). So we set up the equation \(5x-10 + 6x + 3=180\).
\[5x+6x-10 + 3=180\]
\[11x-7 = 180\]

Step2: Solve the equation for \(x\)

Add 7 to both sides of the equation:
\[11x-7+7=180 + 7\]
\[11x=187\]
Divide both sides by 11:
\[x=\frac{187}{11}\]
\[x = 17\]

Answer:

\(x = 17\)