1. **Problem Statement:** We have a pair of parallel lines cut by a transversal, creating 8 angles. We will label 6 of these angles and use angle relationships such as corresponding angles, co-interior angles, and alternate interior angles. 2. **Setup:** Let lines $l$ and $m$ be parallel, and let line $t$ be the transversal cutting them. 3. **Label Angles:** Label the angles formed at the intersection of $t$ with $l$ as $\angle 1, \angle 2, \angle 3, \angle 4$ clockwise starting from the top left. Label the angles formed at the intersection of $t$ with $m$ as $\angle 5, \angle 6, \angle 7, \angle 8$ similarly. 4. **Given Angle Measurements:** Suppose $\angle 1 = 50^\circ$, $\angle 5 = 50^\circ$, and $\angle 4 = 130^\circ$. 5. **Angle Relationships:** - Corresponding angles: $\angle 1$ and $\angle 5$ are equal because lines $l$ and $m$ are parallel. - Alternate interior angles: $\angle 3$ and $\angle 5$ are equal. - Co-interior angles: $\angle 4$ and $\angle 5$ are supplementary, so $\angle 4 + \angle 5 = 180^\circ$. 6. **Find Unknown Angles:** - Since $\angle 1 = 50^\circ$, $\angle 2 = 130^\circ$ (linear pair with $\angle 1$). - $\angle 3 = \angle 5 = 50^\circ$ (alternate interior angles). - $\angle 4 = 130^\circ$ (given), so $\angle 8 = 50^\circ$ (corresponding to $\angle 4$). - $\angle 6 = 130^\circ$ (linear pair with $\angle 5$). - $\angle 7 = 50^\circ$ (corresponding to $\angle 3$). 7. **Summary:** The six labelled angles are $\angle 1 = 50^\circ$, $\angle 3 = 50^\circ$, $\angle 4 = 130^\circ$, $\angle 5 = 50^\circ$, $\angle 6 = 130^\circ$, and $\angle 7 = 50^\circ$. This demonstrates the use of parallel lines and transversal angle relationships.