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 triangle angle sum rule:** The sum of the interior angles in any triangle is always $180^\circ$. 3. **Check the given angles:** The angles given are $287^\circ$ and $119^\circ$. Since $287^\circ$ is greater than $180^\circ$, it cannot be an interior angle of a triangle. This suggests the $287^\circ$ angle is an exterior angle. 4. **Use the exterior angle theorem:** The exterior angle is equal to the sum of the two opposite interior angles. Here, $287^\circ$ is the exterior angle, and the two opposite interior angles are $p$ and $119^\circ$. 5. **Set up the equation:** $$287 = p + 119$$ 6. **Solve for $p$:** $$p = 287 - 119$$ $$p = 168$$ 7. **Conclusion:** The size of angle $p$ is $168^\circ$. This makes sense because the interior angle $p$ plus the adjacent interior angle $119^\circ$ sum to the exterior angle $287^\circ$.