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 top parallel line, the top, left angle measure is x degrees. Where the third line crosses the bottom parallel line, the top, left angle measure is 116 degrees.
\[116^\circ\]
\[x^\circ\]
\[x =\]
\[^\circ\]
Two parallel lines with a third line intersecting each line. Where the third line crosses the top parallel line, the top, left angle measure is x degrees. Where the third line crosses the bottom parallel line, the top, left angle measure is 116 degrees.
\[116^\circ\]
\[x^\circ\]
\[x =\]
\[^\circ\]
Answers
GPT-4o mini
To solve for \(x\) in the scenario described, we can use the property of alternate interior angles formed when a transversal intersects two parallel lines.
From the given information:
- The angle measures at the intersection of the transversal with the parallel lines are:
- \(x^\circ\) on the top line
- \(116^\circ\) on the bottom line
Since the two lines are parallel, we can apply the alternate interior angles theorem. This theorem states that if a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.
The angles \(x\) and \(116^\circ\) are alternate interior angles. Therefore, we have:
\[
x = 116^\circ
\]
Thus, the value of \(x\) is:
\[
\boxed{116}
\]
From the given information:
- The angle measures at the intersection of the transversal with the parallel lines are:
- \(x^\circ\) on the top line
- \(116^\circ\) on the bottom line
Since the two lines are parallel, we can apply the alternate interior angles theorem. This theorem states that if a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.
The angles \(x\) and \(116^\circ\) are alternate interior angles. Therefore, we have:
\[
x = 116^\circ
\]
Thus, the value of \(x\) is:
\[
\boxed{116}
\]