Question

given m||n, find the value of x. (4x - 6)° (4x + 10)°

Explanation:

Step1: Use angle - relationship of parallel lines

Since \(m\parallel n\), the two given angles \((4x - 6)^{\circ}\) and \((4x+10)^{\circ}\) are supplementary (linear - pair of angles). So, \((4x - 6)+(4x + 10)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4x+4x-6 + 10=180\), which simplifies to \(8x+4 = 180\).

Step3: Isolate the variable term

Subtract 4 from both sides of the equation: \(8x=180 - 4\), so \(8x=176\).

Step4: Solve for x

Divide both sides by 8: \(x=\frac{176}{8}=22\).

Answer:

\(x = 22\)