1. **Stating the problem:** We have a 7-sided polygon (heptagon) with sides 165, 150, 123, 100, 170, and two unknown sides labeled $x+11$ and $x$. We want to find the value of $x$. 2. **Formula for the sum of interior angles:** The sum of interior angles of an $n$-sided polygon is given by $$180(n-2)$$ degrees. 3. **Important note:** The sum of the lengths of the sides is not equal to the sum of the interior angles. The equation you wrote, $2x + 708 = 180(5)$, seems to confuse side lengths with angle sums. The number 5 in $180(5)$ corresponds to $n-2$ where $n=7$. 4. **Clarifying the problem:** If you want to find $x$ based on the perimeter (sum of sides), you should add all sides and set equal to the perimeter. If you want to use the interior angle sum formula, it relates to angles, not side lengths. 5. **Assuming you want to find $x$ from the perimeter:** Sum of known sides: $$165 + 150 + 123 + 100 + 170 = 708$$ Sum of unknown sides: $$x + (x + 11) = 2x + 11$$ Total perimeter: $$708 + 2x + 11 = 719 + 2x$$ 6. **If you have an equation relating perimeter to something else, please clarify.** 7. **If the equation $2x + 708 = 180(5)$ is given, solve for $x$:** Calculate right side: $$180(5) = 900$$ Equation: $$2x + 708 = 900$$ Subtract 708 from both sides: $$2x = 900 - 708 = 192$$ Divide both sides by 2: $$x = \frac{192}{2} = 96$$ **Final answer:** $$x = 96$$