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In the figure, we are given that \( PQ \parallel RS \) and that \( \angle MON = 25^\circ \). The problem asks us to find the measure of \( \angle LOM \).

Since \( PQ \parallel RS \), the lines form a pair of corresponding angles. This means that the angle \( \angle MON \), which is 25°, corresponds to \( \angle LOM \) because these are alternate interior angles formed by the transversal line passing through the parallel lines \( PQ \) and \( RS \).

Thus, \( \angle LOM = \angle MON = 25^\circ \).

So, the measure of \( \angle LOM \) is **25 degrees**.

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Would you like further details or have any other questions?

Here are some relative questions for deeper understanding:

1. Why are alternate interior angles equal when two parallel lines are crossed by a transversal?
2. What other angles in the figure can be deduced based on the given parallel lines and transversal?
3. How would the problem change if \( PQ \not\parallel RS \)?
4. Can we use any properties of corresponding angles in this diagram?
5. How would you solve this if \( \angle MON \) were not given?

**Tip:** When working with parallel lines and transversals, always look for corresponding, alternate interior, and co-interior angle relationships!

In the adjacent figure, PQ || RS and m∠MON = 25°. Find m∠LOM (in degrees).

Learn how to find the measure of angle LOM in a diagram where PQ is parallel to RS and angle MON is given as 25°. The solution uses the Alternate Interior Angles Theorem to show that m∠LOM = 25°. Suitable for students in Grades 7-9.

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