Question

given m||n, find the value of x.
answer attempt 1 out of 3
x =

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the two given angles \((2x - 2)^{\circ}\) and \((2x-30)^{\circ}\) are same - side interior angles, and they are supplementary, so \((2x - 2)+(2x-30)=180\).

Step2: Simplify the left - hand side

Combine like terms: \(2x-2 + 2x-30=(2x+2x)+(-2 - 30)=4x-32\). So the equation becomes \(4x-32 = 180\).

Step3: Isolate the variable term

Add 32 to both sides of the equation: \(4x-32 + 32=180 + 32\), which simplifies to \(4x=212\).

Step4: Solve for \(x\)

Divide both sides by 4: \(x=\frac{212}{4}=53\).

Answer:

\(x = 53\)