1. **State the problem:** We are given a triangle with two known angles, $110^\circ$ and $20^\circ$, and we need to find the measure of the third angle. 2. **Formula used:** The sum of the interior angles of any triangle is always $180^\circ$. This means: $$m \angle_1 + m \angle_2 + m \angle_3 = 180^\circ$$ 3. **Apply the formula:** Let the unknown angle be $x$. Then: $$110^\circ + 20^\circ + x = 180^\circ$$ 4. **Simplify:** $$130^\circ + x = 180^\circ$$ 5. **Solve for $x$:** $$x = 180^\circ - 130^\circ$$ $$x = 50^\circ$$ 6. **Conclusion:** The measure of the third angle is $50^\circ$. This method applies to any triangle: add the known angles and subtract from $180^\circ$ to find the missing angle.