1. **State the problem:** We need to find the sizes of angles $p$ and $r$ given that there are three parallel lines cut by perpendicular transversal lines, and one angle is $126^\circ$. 2. **Angle facts used:** - Corresponding angles between parallel lines are equal. - Angles on a straight line sum to $180^\circ$. - Since the transversal lines are perpendicular to the parallel lines, angles formed are right angles ($90^\circ$). 3. **Find angle $p$:** - Angle $p$ is vertically opposite to the $126^\circ$ angle (or corresponding to it on the next parallel line), so $p = 126^\circ$. 4. **Find angle $r$:** - Angle $r$ and angle $p$ are on a straight line, so their sum is $180^\circ$. - Calculate $r = 180^\circ - p = 180^\circ - 126^\circ = 54^\circ$. **Final answers:** $$p = 126^\circ$$ $$r = 54^\circ$$