Question

3 the figure shows two lines cut by a transversal. which value of x shows that the lines are parallel? a x = 36 b x = 42 c x = 48 d x = 72 noah chose a as the correct answer. how might he have gotten that answer?

Explanation:

Step1: Use the property of alternate - interior angles

If two lines are parallel, then alternate - interior angles are equal. So, we set up the equation \(x = 2x-36\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(0=2x - 36-x\).
Simplify to get \(x = 36\). But wait, this is wrong. The correct property is that if two lines are parallel, then consecutive - interior angles are supplementary. So the correct equation is \(x+(2x - 36)=180\).

Step3: Solve the correct equation

Expand: \(x + 2x-36=180\).
Combine like terms: \(3x-36 = 180\).
Add 36 to both sides: \(3x=180 + 36=216\).
Divide both sides by 3: \(x=\frac{216}{3}=72\).

Noah might have thought that the angles \(x\) and \(2x - 36\) are alternate - interior angles. But in reality, for the lines to be parallel, \(x\) and \(2x - 36\) are consecutive - interior angles (they are on the same side of the transversal and between the two lines).

Answer:

D. \(x = 72\)