Question

given m||n, find the value of x.

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the given angles \((4x + 3)^{\circ}\) and \((x- 3)^{\circ}\) are same - side interior angles, and same - side interior angles are supplementary. So, \((4x + 3)+(x - 3)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4x+3+x - 3=4x+x+(3 - 3)=5x\). So the equation becomes \(5x=180\).

Step3: Solve for \(x\)

Divide both sides of the equation \(5x = 180\) by 5. We get \(x=\frac{180}{5}=36\).

Answer:

\(x = 36\)