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The image you uploaded shows a diagram with two lines, \( L \) and \( M \), and you're asked to determine if \( L \parallel M \) (whether lines \( L \) and \( M \) are parallel). 

There are two angles marked in the diagram:
- One angle is labeled \( 53^\circ \).
- Another angle is labeled \( 127^\circ \).

These angles are consecutive interior angles (or co-interior angles) formed by a transversal crossing lines \( L \) and \( M \).

To determine if \( L \parallel M \), we use the property of co-interior angles. If the sum of the two consecutive interior angles equals \( 180^\circ \), the lines are parallel.

Let's check:

\[
53^\circ + 127^\circ = 180^\circ
\]

Since the sum is \( 180^\circ \), lines \( L \) and \( M \) are parallel.

Let me know if you'd like more details or have any questions.

Here are some relative questions to deepen your understanding:
1. What is the relationship between alternate interior angles when two lines are parallel?
2. How do corresponding angles behave when lines are parallel?
3. What are the conditions for two lines to be perpendicular?
4. Can co-interior angles be used to check if lines are perpendicular? Why or why not?
5. How would the result change if the sum of the angles was not \( 180^\circ \)?

**Tip:** When working with angles formed by a transversal, remember the different angle pairs (alternate interior, corresponding, and co-interior) to help identify relationships between the lines.

Check whether lines L and M are parallel or not, given that the consecutive angles are 53° and 127°.

Learn how to determine if lines L and M are parallel by using co-interior angles. Given angles of 53° and 127°, this problem demonstrates the Co-interior Angle Theorem and how the sum of these angles equals 180°, proving the lines are parallel. Suitable for students in Grades 8-10.

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