1. **State the problem:** We have a pentagon with five sides and four known angles: 50°, 120°, 80°, and one unknown angle marked with a question mark (?). We need to find the value of this unknown angle. 2. **Formula for the sum of interior angles of a polygon:** The sum of interior angles of an n-sided polygon is given by: $$\text{Sum of interior angles} = (n-2) \times 180^\circ$$ For a pentagon, $n=5$, so: $$\text{Sum} = (5-2) \times 180^\circ = 3 \times 180^\circ = 540^\circ$$ 3. **Use the given angles:** The sum of all five interior angles must be 540°. We know four angles: 50°, 120°, 80°, and the unknown angle $x$. Let the fifth angle be $y$. 4. **Use the property of equal-length sides:** The polygon has two pairs of equal-length sides, which implies that the angles opposite those sides are equal. Since the unknown angle is adjacent to the 120° angle and between two equal-length sides, the unknown angle $x$ is equal to the angle opposite it, which is 50° (because the pair of equal sides opposite to 50° and $x$). 5. **Calculate the unknown angle:** Since $x = 50^\circ$, the sum of the known angles is: $$50^\circ + 120^\circ + 80^\circ + 50^\circ = 300^\circ$$ 6. **Find the fifth angle $y$:** $$y = 540^\circ - 300^\circ = 240^\circ$$ 7. **Conclusion:** The unknown angle $x$ is $50^\circ$. **Final answer:** $$\boxed{50^\circ}$$