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 bottom, right most angle measure is 129 degrees. Where the third line crosses the right most parallel line, the top, left angle measure is x degrees.
\[129^\circ\]
\[x^\circ\]
\[x = \]
\[^\circ\]
Two parallel lines with a third line intersecting each line. Where the third line crosses the left most parallel line, the bottom, right most angle measure is 129 degrees. Where the third line crosses the right most parallel line, the top, left angle measure is x degrees.
\[129^\circ\]
\[x^\circ\]
\[x = \]
\[^\circ\]
Answers
GPT-4o mini
To solve for \( x \), we can use the properties of parallel lines and transversals.
When a transversal intersects two parallel lines, it creates pairs of alternate interior angles and corresponding angles that are congruent. Here, we have the following information:
1. The bottom right angle at the intersection of the transversal and the left parallel line measures \( 129^\circ \).
2. We need to find the angle \( x \) at the intersection of the transversal and the right parallel line.
Since the angle of \( 129^\circ \) is an exterior angle on the left line, the angle that is adjacent to it on the same side of the transversal (top right angle of the left parallel line) can be calculated as follows:
- The sum of the angles on a straight line is \( 180^\circ \). Therefore, the adjacent angle (which we can call \( y \)) can be calculated as:
\[
y = 180^\circ - 129^\circ = 51^\circ
\]
Now, the angle \( y \) (which measures \( 51^\circ \)) is an alternate interior angle to the angle \( x \) (the top left angle where the transversal intersects the right parallel line).
Since alternate interior angles are equal, we have:
\[
x = 51^\circ
\]
Thus, the measure of angle \( x \) is:
\[
\boxed{51^\circ}
\]
When a transversal intersects two parallel lines, it creates pairs of alternate interior angles and corresponding angles that are congruent. Here, we have the following information:
1. The bottom right angle at the intersection of the transversal and the left parallel line measures \( 129^\circ \).
2. We need to find the angle \( x \) at the intersection of the transversal and the right parallel line.
Since the angle of \( 129^\circ \) is an exterior angle on the left line, the angle that is adjacent to it on the same side of the transversal (top right angle of the left parallel line) can be calculated as follows:
- The sum of the angles on a straight line is \( 180^\circ \). Therefore, the adjacent angle (which we can call \( y \)) can be calculated as:
\[
y = 180^\circ - 129^\circ = 51^\circ
\]
Now, the angle \( y \) (which measures \( 51^\circ \)) is an alternate interior angle to the angle \( x \) (the top left angle where the transversal intersects the right parallel line).
Since alternate interior angles are equal, we have:
\[
x = 51^\circ
\]
Thus, the measure of angle \( x \) is:
\[
\boxed{51^\circ}
\]