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 \(m\) and \(n\) are cut by a transversal, the corresponding angles are equal. Here, \((6x - 27)^{\circ}\) and \((8x-3)^{\circ}\) are corresponding angles, so we set up the equation \(6x - 27=8x - 3\).

Step2: Rearrange the equation

Subtract \(6x\) from both sides: \(- 27=8x-6x - 3\), which simplifies to \(-27 = 2x-3\).

Step3: Solve for \(x\)

Add 3 to both sides: \(-27 + 3=2x\), so \(-24 = 2x\). Then divide both sides by 2: \(x=\frac{-24}{2}=-12\). But angles cannot be negative in this context, we may have mis - identified the angle relationship. In fact, these are same - side interior angles which are supplementary. So the correct equation is \((6x - 27)+(8x - 3)=180\).

Step4: Simplify the new equation

Combine like terms: \(6x+8x-27 - 3=180\), which gives \(14x-30 = 180\).

Step5: Isolate \(x\)

Add 30 to both sides: \(14x=180 + 30=210\). Then divide both sides by 14: \(x=\frac{210}{14}=15\).

Answer:

\(x = 15\)