Question

The parking spaces in a city lot were created by painting rows of parallel line segments, then painting a line that cuts through each of the parallel segments. A sketch of two parking spaces is shown below.

2 diagonal parallel lines are cut by a horizontal transversal. Where the first parallel line intersects the transversal, the top right angle is angle 1. Where the second parallel line intersects the transversal, the top left angle is angle 2.
If m∠2 = 115°, what is m∠1?

Answer 1

To find \( m∠1 \), we will use the properties of angles formed by parallel lines cut by a transversal.

Given that \( m∠2 = 115° \), we can observe the relationship between the angles formed:

1. Since the diagonal lines are parallel and the line cutting through them is transversal, angles that are on opposite sides of the transversal (and inside the parallel lines) are called alternate interior angles.
2. \( m∠1 \) and \( m∠2 \) are alternate interior angles.

By the property of alternate interior angles, we know that alternate interior angles are equal when two parallel lines are cut by a transversal:

\[
m∠1 = m∠2
\]

Thus, since \( m∠2 = 115° \):

\[
m∠1 = 115°
\]

Therefore, the measure of angle 1 is:

\[
\boxed{115°}
\]