Question

Oak Street and Elm Street run parallel to each other. When Main Street intersects them, it forms exterior ∠8, measuring 60°. What is the measure of ∠2?

A line labelled Main transecting two parallel lines labelled Oak and Elm. Text that reads: Angle 1, 2, 3, 4 formed at the point Main intersects with Oak. Angles 5, 6, 7, 8 formed at the point Main intersects with Elm.
A.
60°
B.
120°
C.
80°
D.
130°

Answer 1

To find the measure of ∠2, we need to use the properties of angles formed when a transversal intersects parallel lines.

Given:
- Exterior angle ∠8 measures 60°.
- The angles around the points of intersection with the parallel lines (Oak and Elm) have specific relationships.

Since Main Street intersects the parallel lines Oak and Elm, we can establish the following relationships among the angles:

1. ∠8 and ∠7 are consecutive interior angles on the same side of the transversal (Main Street) and sum to 180°.
2. Thus, if ∠8 = 60°, then:
\[
∠7 = 180° - ∠8 = 180° - 60° = 120°.
\]

3. Now, ∠2 is corresponding to ∠7 (since they are on the same side of the transversal and the same relative position at the intersections with the parallels). Therefore, we have:
\[
∠2 = ∠7 = 120°.
\]

Thus, the measure of ∠2 is **120°**.

So the answer is:
**B. 120°**