In the image, you are asked to find the measures of two angles, $\angle 1$ and $\angle 2$, and justify the answer.

Step-by-step solution:

1. Identify given information:

   • $\angle 2$ is marked as 78°.
   • The lines $l$ and $m$ appear to be parallel, as they are cut by the transversal $t$.

2. Determine $m \angle 2$:

   • From the diagram, $m \angle 2 = 78^\circ$, since this angle is directly given.

3. Find $m \angle 1$:

   • $\angle 1$ and $\angle 2$ are alternate interior angles, since they are on opposite sides of the transversal $t$ and between the parallel lines $l$ and $m$.
   • By the Alternate Interior Angles Theorem, if two parallel lines are cut by a transversal, alternate interior angles are congruent.
   • Therefore, $m \angle 1 = m \angle 2$.
   • Hence, $m \angle 1 = 78^\circ$.

Conclusion:

• $m \angle 1 = 78^\circ$
• $m \angle 2 = 78^\circ$

Both are justified by the Alternate Interior Angles Theorem.

Do you need more details on any part of the solution or have any specific questions?

Here are five related questions to further expand your understanding:

1. What is the definition of alternate interior angles?
2. Can two non-parallel lines form congruent alternate interior angles?
3. What is the difference between corresponding angles and alternate interior angles?
4. How would the solution change if $l$ and $m$ were not parallel?
5. What is the Converse of the Alternate Interior Angles Theorem?

Tip: When working with parallel lines, always check the position of the transversal to identify congruent angles (like alternate interior or corresponding angles).