1. **State the problem:** We are given a triangle with angles measuring 81°, $x$°, and 40°. We need to find the value of $x$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always 180°. This can be written as: $$81 + x + 40 = 180$$ 3. **Set up the equation:** $$81 + x + 40 = 180$$ 4. **Combine like terms:** $$121 + x = 180$$ 5. **Isolate $x$ by subtracting 121 from both sides:** $$\cancel{121} + x - \cancel{121} = 180 - 121$$ $$x = 59$$ 6. **Conclusion:** The value of $x$ is 59 degrees. This means the triangle's angles are 81°, 59°, and 40°, which sum to 180° as expected.