In the diagram, we have two parallel lines $\ell_1 \parallel \ell_2$ and a transversal line $t$, which intersects both parallel lines. The angles are numbered from 1 to 8.

To answer the question of which pair of angles are not congruent, we need to use the properties of parallel lines and transversals. Some important angle relationships are:

• Corresponding angles: These are equal. For example, $\angle 1 \cong \angle 5$, $\angle 2 \cong \angle 6$, $\angle 3 \cong \angle 7$, and $\angle 4 \cong \angle 8$.
• Alternate interior angles: These are also equal. For example, $\angle 1 \cong \angle 7$ and $\angle 2 \cong \angle 8$.
• Vertical angles: These are equal as well. For example, $\angle 1 \cong \angle 3$ and $\angle 2 \cong \angle 4$, as well as $\angle 5 \cong \angle 7$ and $\angle 6 \cong \angle 8$.

Conclusion:

Looking at the relationships:

• $\angle 5$ and $\angle 3$ are not congruent because they are neither corresponding angles, alternate interior angles, nor vertical angles.

Would you like further details or have any specific questions?

Related Questions:

1. What are corresponding angles and why are they congruent?
2. How do alternate interior angles behave with parallel lines?
3. What is the difference between vertical angles and adjacent angles?
4. Why do transversals create special angle relationships with parallel lines?
5. How would the situation change if the lines were not parallel?

Tip: Always look for parallel line markings and transversals to identify key angle relationships such as corresponding and alternate interior angles.