Question

if angle four is equal to 4x - 6 , and angle 6 is equal to 2x-12 , solve for x.
diagram: two parallel lines m (top) and n (bottom) cut by a transversal. angles labeled 1,2,3,4 on line m; 5,6,7,8 on line n.
options:
-3
33
16
30

Explanation:

Step1: Identify angle relationship

Angles 4 and 6 are same - side interior angles. If lines \(m\) and \(n\) are parallel (implied by the transversal and angle labeling), same - side interior angles are supplementary, so \(m\angle4 + m\angle6=180^{\circ}\).
Given \(m\angle4 = 4x - 6\) and \(m\angle6=2x - 12\), we set up the equation: \((4x - 6)+(2x - 12)=180\).

Step2: Simplify the left - hand side

Combine like terms: \(4x+2x-6 - 12 = 180\), which simplifies to \(6x-18 = 180\).

Step3: Solve for \(x\)

Add 18 to both sides of the equation: \(6x-18 + 18=180 + 18\), so \(6x=198\).
Divide both sides by 6: \(x=\frac{198}{6}=33\).

Answer:

33