In the diagram, the measures of ∠2, ∠6, and ∠7 are 25°. The measure of ∠1 is 155°. Are lines c and d parallel?

The image depicts two parallel lines and one intersecting line across the parallel lines.
A.
No, because ∠6 and ∠1 are not congruent.
B.
No, because ∠1 and ∠2 are not congruent.
C.
Yes, because ∠2 and ∠6 are congruent.
D.
Yes, because ∠6 and ∠7 are congruent.

1 answer

To determine if lines c and d are parallel, we can utilize the properties of angles formed by a transversal crossing two lines.

Given:

∠2 = 25°
∠6 = 25°
∠7 = 25°
∠1 = 155°

In this situation:

∠1 (155°) is an exterior angle.
∠2 (25°), ∠6 (25°), and ∠7 (25°) are interior angles.

For two lines to be parallel, certain angle relationships must hold:

If two interior angles on the same side of the transversal are supplementary (add up to 180°), then the lines are not parallel.
If two interior angles on opposite sides of the transversal are congruent, then the lines are parallel.

Now, let's see the relationships:

∠1 and ∠2 are on the same side of the transversal. They add up to 155° + 25° = 180°, which means they are supplementary.

Since ∠1 and ∠2 are supplementary, we conclude that lines c and d are not parallel.

The correct answer is: B. No, because ∠1 and ∠2 are not congruent.