Question

if angle four is equal to 4x - 6, and angle 6 is equal to 2x - 12, solve for x.

Explanation:

Step1: Identify angle - relationship

Angle 4 and angle 6 are alternate - interior angles. If lines m and n are parallel, alternate - interior angles are equal. So we set up the equation \(4x - 6=2x - 12\).

Step2: Isolate x - terms

Subtract \(2x\) from both sides of the equation: \((4x - 6)-2x=(2x - 12)-2x\), which simplifies to \(2x-6=-12\).

Step3: Isolate the constant term

Add 6 to both sides of the equation: \((2x - 6)+6=-12 + 6\), resulting in \(2x=-6\).

Step4: Solve for x

Divide both sides of the equation by 2: \(\frac{2x}{2}=\frac{-6}{2}\), so \(x=-3\).

Answer:

A. - 3