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We are given that lines \( l \) and \( m \) are parallel. Also, \( m\angle 1 = 40^\circ \) and \( m\angle 2 = 80^\circ \). We are tasked with finding the measure of \( \angle 3 \).

### Solution:

Since lines \( l \) and \( m \) are parallel, we can apply properties of parallel lines and transversals:

1. **Corresponding angles**: Corresponding angles are equal when a transversal crosses parallel lines.
   - \( \angle 1 \) and \( \angle 3 \) are corresponding angles, as they are on the same side of the transversal and in corresponding positions with respect to the parallel lines \( l \) and \( m \).

   Therefore, \( \angle 3 = \angle 1 \).

2. We know that:
   \[
   m\angle 1 = 40^\circ
   \]
   So, \( m\angle 3 = 40^\circ \).

Thus, the measure of \( \angle 3 \) is \( \boxed{40^\circ} \).

Would you like further explanation on parallel lines and angle relationships?

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Here are 5 related questions for further practice:
1. If \( \angle 1 \) was \( 50^\circ \), what would be the measure of \( \angle 3 \)?
2. What is the sum of the interior angles on the same side of the transversal in this diagram?
3. If \( m\angle 2 = 80^\circ \), what is the corresponding angle to \( \angle 2 \)?
4. How do alternate interior angles behave when two lines are parallel?
5. Can you determine the measure of \( \angle p \) in the diagram?

**Tip**: When dealing with parallel lines, always look for corresponding angles, alternate interior angles, and co-interior angles to find unknown angles.

In this diagram, Lines l and m are parallel to each other, m∠1 = 40° and m∠2 = 80°. What is the measure of ∠3?

Learn how to find the measure of angle 3 in a diagram with parallel lines and transversals, where m∠1 = 40° and m∠2 = 80°. This problem explores key geometry concepts such as corresponding angles and theorems related to parallel lines. Suitable for students in Grades 7-9.

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