Question

line ( s ) intersects lines ( p ) and ( r ) in the figure.
if line ( p ) is parallel to line ( r ), what is the value of ( x )?

Explanation:

Step1: Use the property of alternate exterior angles

When two parallel lines are cut by a transversal, alternate exterior angles are equal. So, \(3x + 8=4x - 6\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(3x+8 - 3x=4x - 6-3x\), which simplifies to \(8=x - 6\).
Then add \(6\) to both sides: \(8 + 6=x-6 + 6\), so \(x = 14\).

Answer:

\(14\)