1. **State the problem:** We need to find which angles have the same measure as angle $\angle 2$ when two parallel lines $m$ and $n$ are intersected by a transversal $t$. 2. **Recall the rules:** - Corresponding angles are equal. - Alternate interior angles are equal. - Vertically opposite angles are equal. 3. **Identify angle $\angle 2$:** It is at the top-right position at the intersection of line $m$ and transversal $t$. 4. **Find angles equal to $\angle 2$:** - $\angle 6$ is corresponding to $\angle 2$ (both top-right at intersections with $m$ and $n$), so $\angle 6 = \angle 2$. - $\angle 3$ is vertically opposite to $\angle 2$, so $\angle 3 = \angle 2$. 5. **Check other angles:** - $\angle 1$ is adjacent to $\angle 2$ but not equal. - $\angle 8$ is neither corresponding nor alternate interior to $\angle 2$. **Final answer:** $\angle 3$ and $\angle 6$ have the same measure as $\angle 2$.