1. **State the problem:** We have a seven-sided polygon (heptagon) with six known interior angles: 117°, 101°, 138°, 110°, 123°, and one unknown angle $x$. We need to find the value of $x$. 2. **Formula used:** 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 heptagon, $n=7$, so: $$\text{Sum} = (7-2) \times 180 = 5 \times 180 = 900^\circ$$ 3. **Calculate the sum of known angles:** $$117 + 101 + 138 + 110 + 123 = 589^\circ$$ 4. **Find the unknown angle $x$:** Since the polygon has seven sides, there are seven interior angles. We know six of them (including the right angle, which is 90°), so the sum of all seven angles is 900°. Add the right angle: $$589 + 90 = 679^\circ$$ Then, $$x = 900 - 679 = 221^\circ$$ 5. **Interpretation:** The unknown angle $x$ measures 221°, which is possible in a concave polygon where some interior angles can be greater than 180°. **Final answer:** $$x = 221^\circ$$