5. use the following diagram to identify:
the transversal ______
a pair of vertical angles ______
a pair of adjacent angles ______
a pair of supplementary angles ______
a pair of alternate interior angles ______

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# Brief Explanations:
- **Transversal**: A transversal is a line that intersects two or more other lines. In the given diagram, line $ n $ intersects lines $ l $ and $ m $, so $ n $ is the transversal.
- **Vertical Angles**: Vertical angles are opposite angles formed by the intersection of two lines. For example, $ \angle 1 $ and $ \angle 4 $ are not vertical angles. But $ \angle 1 $ and $ \angle 3 $ are not either. $ \angle 3 $ and $ \angle 4 $ form a linear - pair. $ \angle 1 $ and $ \angle 2 $ form a linear - pair. $ \angle 3 $ and $ \angle 5 $ are alternate interior angles (if lines $ l$ and $m$ are parallel). $ \angle 1 $ and $ \angle 5 $ are corresponding angles (if lines $ l$ and $m$ are parallel). $ \angle 2 $ and $ \angle 4 $ are vertical angles (formed by the intersection of line $ l$ and transversal $ n$).
- **Adjacent Angles**: Adjacent angles have a common side and a common vertex and no common interior points. $ \angle 1 $ and $ \angle 2 $ share a common side (the non - common sides form a line) and a common vertex.
- **Supplementary Angles**: Supplementary angles add up to $ 180^{\circ}$. $ \angle 1 $ and $ \angle 2 $ form a linear - pair (since they are adjacent and their non - common sides form a straight line), so $ \angle 1+\angle 2 = 180^{\circ}$.
- **Alternate Interior Angles**: Alternate interior angles are between the two lines ($ l$ and $m$) and on opposite sides of the transversal ($n$). $ \angle 3 $ and $ \angle 5 $ are between lines $ l$ and $m$ and on opposite sides of transversal $n$.

# Answer:
- The transversal: $n$
- A pair of vertical angles: $ \angle 2$ and $ \angle 4$ (or $ \angle 1$ and $ \angle 3$, $ \angle 5$ and $ \angle 6$, $ \angle 7$ and $ \angle 8$)
- A pair of adjacent angles: $ \angle 1$ and $ \angle 2$ (or $ \angle 2$ and $ \angle 4$, $ \angle 3$ and $ \angle 4$, $ \angle 1$ and $ \angle 3$, $ \angle 5$ and $ \angle 6$, $ \angle 6$ and $ \angle 8$, $ \angle 7$ and $ \angle 8$, $ \angle 5$ and $ \angle 7$)
- A pair of supplementary angles: $ \angle 1$ and $ \angle 2$ (or $ \angle 2$ and $ \angle 4$, $ \angle 3$ and $ \angle 4$, $ \angle 1$ and $ \angle 3$, $ \angle 5$ and $ \angle 6$, $ \angle 6$ and $ \angle 8$, $ \angle 7$ and $ \angle 8$, $ \angle 5$ and $ \angle 7$)
- A pair of alternate interior angles: $ \angle 3$ and $ \angle 5$ (or $ \angle 4$ and $ \angle 6$)

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