1. **State the problem:** We need to find the sizes of angles $t$, $s$, and $r$ in a figure with three parallel lines cut by two transversals, given angles $48^\circ$ and $120^\circ$. 2. **Recall angle rules:** - Alternate interior angles are equal when lines are parallel. - Angles on a straight line sum to $180^\circ$. - Corresponding angles are equal. 3. **Find angle $s$:** Given $x = 120^\circ$ and $s = x$ by alternate interior angles, so $$s = 120^\circ.$$ 4. **Find angle $t$:** Angles $s$ and $t$ are on a straight line, so $$s + t = 180^\circ.$$ Substitute $s = 120^\circ$: $$120^\circ + t = 180^\circ.$$ Subtract $120^\circ$ from both sides: $$\cancel{120^\circ} + t = 180^\circ - \cancel{120^\circ}$$ $$t = 60^\circ.$$ 5. **Find angle $r$:** Angle $r$ and the given $120^\circ$ angle are on a straight line, so $$r + 120^\circ = 180^\circ.$$ Subtract $120^\circ$ from both sides: $$\cancel{120^\circ} + r = 180^\circ - \cancel{120^\circ}$$ $$r = 60^\circ.$$ **Final answers:** $$s = 120^\circ, \quad t = 60^\circ, \quad r = 60^\circ.$$