1. **State the problem:** We have two parallel lines cut by a transversal, creating angles labeled $r$, $s$, and $t$, with given angles $120^\circ$ and $48^\circ$. We need to find the sizes of $r$, $s$, and $t$ with reasons. 2. **Recall important rules:** - Corresponding angles between parallel lines are equal. - Alternate interior angles between parallel lines are equal. - Angles on a straight line sum to $180^\circ$. 3. **Find angle $r$:** Angle $r$ and the $120^\circ$ angle are on a straight line, so $$r + 120^\circ = 180^\circ$$ $$r = 180^\circ - 120^\circ = 60^\circ$$ Reason: Angles on a straight line sum to $180^\circ$. 4. **Find angle $s$:** Angle $s$ corresponds to the $48^\circ$ angle on the other parallel line (same relative position), so $$s = 48^\circ$$ Reason: Corresponding angles between parallel lines are equal. 5. **Find angle $t$:** Angles $s$ and $t$ are adjacent and form a straight line, so $$s + t = 180^\circ$$ Substitute $s=48^\circ$: $$48^\circ + t = 180^\circ$$ $$t = 180^\circ - 48^\circ = 132^\circ$$ Reason: Angles on a straight line sum to $180^\circ$. **Final answers:** $$r = 60^\circ, \quad s = 48^\circ, \quad t = 132^\circ$$