Question

a pair of parallel lines is cut by a transversal. if (mangle a=(4x - 2)^{circ}) and (mangle b=(6x - 20)^{circ}), what is the value of x? 34 20.2 11.2 9

Explanation:

Step1: Identify angle - relationship

When parallel lines are cut by a transversal, corresponding angles (or alternate - interior/alternate - exterior angles depending on the position) are equal. Here, assume ∠A and ∠B are equal. So, we set up the equation \(4x - 2=6x - 20\).

Step2: Rearrange the equation

Subtract \(4x\) from both sides: \(- 2=6x-4x - 20\), which simplifies to \(-2 = 2x-20\).

Step3: Solve for \(x\)

Add 20 to both sides: \(-2 + 20=2x\), so \(18 = 2x\). Then divide both sides by 2: \(x=\frac{18}{2}=9\).

Answer:

9