1. **State the problem:** We need to find the size of angle $p$ in a triangle where the other two angles are $287^\circ$ and $119^\circ$. 2. **Recall the rule:** The sum of the interior angles of any triangle is always $180^\circ$. 3. **Write the equation:** $$287^\circ + 119^\circ + p = 180^\circ$$ 4. **Add the known angles:** $$406^\circ + p = 180^\circ$$ 5. **Isolate $p$:** $$p = 180^\circ - 406^\circ$$ 6. **Calculate $p$:** $$p = -226^\circ$$ 7. **Interpretation:** Since angle $p$ cannot be negative in a triangle, the given angles do not form a valid triangle. Possibly, the $287^\circ$ angle is an exterior angle or the figure is not a triangle. **Final answer:** The given angles cannot form a triangle, so angle $p$ is not defined under these conditions.