Question

the figure shows two lines cut by a transversal. which value of x shows that the lines are parallel? x = (4x - 10)° (x + 20)°

Explanation:

Step1: Use the property of alternate exterior angles

When two lines are parallel, alternate exterior angles are equal. So, \(4x - 10=x + 20\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(4x-x-10=x - x+ 20\), which simplifies to \(3x-10 = 20\).
Add \(10\) to both sides: \(3x-10 + 10=20 + 10\), getting \(3x=30\).
Divide both sides by \(3\): \(x=\frac{30}{3}\).

Answer:

\(10\)