Question

the figure shows two lines cut by a transversal. which value of x shows that the lines are parallel? x = (2x + 17)° 75°

Explanation:

Step1: Set up the equation

When two lines are parallel and cut by a transversal, the sum of consecutive interior angles is \(180^{\circ}\). So, \((2x + 17)+75=180\).

Step2: Simplify the equation

First, combine like - terms: \(2x+17 + 75=2x + 92\). The equation becomes \(2x+92 = 180\).

Step3: Solve for \(x\)

Subtract \(92\) from both sides: \(2x=180 - 92\), so \(2x = 88\). Then divide both sides by \(2\): \(x=\frac{88}{2}\).

Answer:

\(29\)