1. **State the problem:** We have a convex pentagon with interior angles 82°, 129°, 121°, 147°, and an unknown angle $x$. We need to find $x$. 2. **Formula for sum of interior angles of a polygon:** The sum of interior angles of an $n$-sided polygon is given by: $$\text{Sum} = (n-2) \times 180^\circ$$ For a pentagon, $n=5$, so: $$\text{Sum} = (5-2) \times 180^\circ = 3 \times 180^\circ = 540^\circ$$ 3. **Set up the equation:** The sum of all interior angles must be 540°: $$82^\circ + 129^\circ + 121^\circ + 147^\circ + x = 540^\circ$$ 4. **Add the known angles:** $$82 + 129 + 121 + 147 = 479$$ 5. **Solve for $x$:** $$x = 540 - 479$$ $$x = 61$$ 6. **Answer:** The value of $x$ is $61^\circ$.