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

Angles 4 and 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: $4x-2x - 6=2x-2x - 12$, which simplifies to $2x - 6=-12$.

Step3: Isolate the constant

Add 6 to both sides: $2x-6 + 6=-12 + 6$, resulting in $2x=-6$.

Step4: Solve for x

Divide both sides by 2: $\frac{2x}{2}=\frac{-6}{2}$, so $x=-3$.

Answer:

C. -3