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 x degrees. Where the third line crosses the right most parallel line, the bottom, left angle measure is 114 degrees.
\[114^\circ\]
\[x^\circ\]
\[x = \]
\[^\circ\]
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 x degrees. Where the third line crosses the right most parallel line, the bottom, left angle measure is 114 degrees.
\[114^\circ\]
\[x^\circ\]
\[x = \]
\[^\circ\]
Answers
GPT-4o mini
Given two parallel lines intersected by a transversal, we can analyze the angles formed by this intersection.
1. **Understanding the Angles**:
- The angle on the leftmost parallel line is labeled as \( x \) degrees.
- The angle on the rightmost parallel line is given as \( 114 \) degrees.
2. **Using Corresponding Angles**:
- Since the two lines are parallel and the third line is a transversal, the angles corresponding to each other are equal. Specifically, the angle that corresponds to \( 114^\circ \) on the leftmost line is \( x \).
3. **Applying the Angle Relationship**:
- Angles on the same side of the transversal (which are consecutive interior angles) add up to \( 180^\circ \). Thus, we can use the relationship:
\[
x + 114^\circ = 180^\circ
\]
4. **Solving for \( x \)**:
- Rearranging the equation to isolate \( x \):
\[
x = 180^\circ - 114^\circ
\]
\[
x = 66^\circ
\]
Thus, the measure of angle \( x \) is \( \boxed{66} \) degrees.
1. **Understanding the Angles**:
- The angle on the leftmost parallel line is labeled as \( x \) degrees.
- The angle on the rightmost parallel line is given as \( 114 \) degrees.
2. **Using Corresponding Angles**:
- Since the two lines are parallel and the third line is a transversal, the angles corresponding to each other are equal. Specifically, the angle that corresponds to \( 114^\circ \) on the leftmost line is \( x \).
3. **Applying the Angle Relationship**:
- Angles on the same side of the transversal (which are consecutive interior angles) add up to \( 180^\circ \). Thus, we can use the relationship:
\[
x + 114^\circ = 180^\circ
\]
4. **Solving for \( x \)**:
- Rearranging the equation to isolate \( x \):
\[
x = 180^\circ - 114^\circ
\]
\[
x = 66^\circ
\]
Thus, the measure of angle \( x \) is \( \boxed{66} \) degrees.