To determine the correct value of \( x \) that makes lines \( m \) and \( n \) parallel, you need to apply one of the theorems regarding angles formed by a transversal intersecting two lines.
You need to check which pairs of angles are represented in the image and their relationships.
-
If the angles are consecutive interior angles, then use the Consecutive Interior Angles Converse Theorem, which states that if two lines are cut by a transversal and the consecutive interior angles are supplementary (i.e., they add up to 180 degrees), then the lines are parallel.
-
If the angles are alternate interior angles, then use the Alternate Interior Angles Converse Theorem, which states that if two lines are cut by a transversal and the alternate interior angles are equal, then the lines are parallel.
Assuming the relationship is that you found, whether consecutive or alternate interior angles leads to a conclusion, just pick the value of \( x \) (either 5 or 10) based on those angle measures and based on the theorem you are using.
Once you have solved for \( x \), you can choose the appropriate response based on the relationship.
If \( x = 5 \) leads to the necessary relationship for parallel lines:
- "If \( x \) is equal to 5, then \( m \parallel n \) by the Consecutive Interior Angles Converse Theorem" or "If ( x = 5, then m∥n by the Alternate Interior Angles Converse Theorem" could be correct depending on the angles provided.
If \( x = 10 \) leads to the required condition for parallel lines:
- "If \( x \) is equal to 10, then \( m \parallel n \) by the Consecutive Interior Angles Converse Theorem" or "If ( x = 10, then m∥n by the Alternate Interior Angles Converse Theorem" would be valid.
Ultimately, you should choose the option that corresponds to the correct theorem and the value of \( x \) derived from the angle measures shown in the image.
1 answer