1. **State the problem:** We have a triangle with angles $\alpha = 90^\circ$ and $\beta = 40^\circ$. We need to find the third angle $\gamma$. 2. **Formula used:** The sum of the interior angles in any triangle is always $180^\circ$. 3. **Apply the formula:** $$\alpha + \beta + \gamma = 180^\circ$$ 4. **Substitute known values:** $$90^\circ + 40^\circ + \gamma = 180^\circ$$ 5. **Simplify:** $$130^\circ + \gamma = 180^\circ$$ 6. **Isolate $\gamma$:** $$\gamma = 180^\circ - 130^\circ$$ 7. **Calculate:** $$\gamma = 50^\circ$$ **Final answer:** The third angle $\gamma$ is $50^\circ$.