Question
Below are two parallel lines with a third line intersecting them.
Two parallel lines with a third line intersecting each line. Where the third line crosses the left most parallel line, the top, right most angle measure is x degrees. Where the third line crosses the right most parallel line, the bottom, left angle measure is 107 degrees.
\[107^\circ\]
\[x^\circ\]
\[x = \]
\[^\circ\]
Two parallel lines with a third line intersecting each line. Where the third line crosses the left most parallel line, the top, right most angle measure is x degrees. Where the third line crosses the right most parallel line, the bottom, left angle measure is 107 degrees.
\[107^\circ\]
\[x^\circ\]
\[x = \]
\[^\circ\]
Answers
GPT-4o mini
When a transversal intersects two parallel lines, it creates several pairs of corresponding, alternate interior, and exterior angles.
Given:
1. The angle formed at the left parallel line, where the transversal intersects it, is \(x^\circ\).
2. The angle formed at the right parallel line, where the transversal intersects it, is \(107^\circ\).
These two angles are alternate interior angles because they are on opposite sides of the transversal and within the two parallel lines.
Since alternate interior angles are equal when a transversal intersects parallel lines, we have:
\[
x = 107
\]
Therefore:
\[
x = 107^\circ
\]
Given:
1. The angle formed at the left parallel line, where the transversal intersects it, is \(x^\circ\).
2. The angle formed at the right parallel line, where the transversal intersects it, is \(107^\circ\).
These two angles are alternate interior angles because they are on opposite sides of the transversal and within the two parallel lines.
Since alternate interior angles are equal when a transversal intersects parallel lines, we have:
\[
x = 107
\]
Therefore:
\[
x = 107^\circ
\]