1. **State the problem:** We need to find the size of angle $p$ in a triangle where the other two angles are $277^\circ$ and $116^\circ$. 2. **Recall the rule:** The sum of the interior angles in any triangle is always $180^\circ$. 3. **Write the equation:** $$p + 277 + 116 = 180$$ 4. **Simplify the sum of known angles:** $$p + 393 = 180$$ 5. **Isolate $p$ by subtracting 393 from both sides:** $$p = 180 - 393$$ 6. **Calculate the value:** $$p = -213$$ 7. **Interpretation:** Since an angle in a triangle cannot be negative, the given angles cannot form a triangle as stated. Possibly, the $277^\circ$ angle is an exterior angle or there is a mistake in the problem setup. **Final answer:** $p = -213^\circ$ (which is not possible for a triangle's interior angle)