Question

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

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal \(t\), the sum of consecutive - interior angles is \(180^{\circ}\). So, \((4x - 6)+(4x + 10)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4x-6 + 4x+10=(4x + 4x)+(-6 + 10)=8x + 4\). The equation becomes \(8x+4 = 180\).

Step3: Solve for \(x\)

Subtract \(4\) from both sides: \(8x+4-4=180 - 4\), which gives \(8x=176\). Then divide both sides by \(8\): \(x=\frac{176}{8}\).

Answer:

\(x = 22\)