Question

a. in the example, what angle forms a pair of alternate interior angles
∠bcf
b. what is the measure of the angle you named in problem 1a?
148°
2 what is the value of x? show your work.
solution

Explanation:

Step1: Use the property of alternate interior angles

When two parallel lines are cut by a transversal, alternate interior angles are congruent. Here, \(4x\) and the angle adjacent to \(140^{\circ}\) (which is \(180 - 140=40^{\circ}\)) are related. Wait, no, actually, when two parallel lines are cut by a transversal, \(4x\) and \(140^{\circ}\) are supplementary (consecutive interior angles). So \(4x+140 = 180\).

Step2: Solve the equation for \(x\)

Subtract \(140\) from both sides of the equation \(4x+140 = 180\). We get \(4x=180 - 140\), so \(4x = 40\). Then divide both sides by \(4\), \(x=\frac{40}{4}\).

Answer:

\(x = 10\)