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?
°
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?
°
Answers
GPT-4o mini
Given that the two diagonal parallel lines are cut by a horizontal transversal, we can analyze the angles formed at the intersections.
Since angles formed by a transversal with parallel lines have special relationships, we can determine the measure of angle 1 based on the measure of angle 2.
Specifically, angle 1 and angle 2 are alternate interior angles. The alternate interior angles theorem tells us that if two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.
Given that \( m∠2 = 115° \), we have:
\[
m∠1 = m∠2 = 115°
\]
Therefore,
\[
\boxed{115°}
\]
Since angles formed by a transversal with parallel lines have special relationships, we can determine the measure of angle 1 based on the measure of angle 2.
Specifically, angle 1 and angle 2 are alternate interior angles. The alternate interior angles theorem tells us that if two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.
Given that \( m∠2 = 115° \), we have:
\[
m∠1 = m∠2 = 115°
\]
Therefore,
\[
\boxed{115°}
\]