1. **State the problem:** We have a 7-sided polygon (heptagon) with known angles 165, 150, 123, 100, 170, and two unknown angles labeled $x+11$ and $x$. We want to find the value of $x$. 2. **Formula for sum of interior angles:** The sum of interior angles of an $n$-sided polygon is given by: $$\text{Sum} = 180(n-2)$$ where $n=7$ for a heptagon. 3. **Calculate the sum of known angles and set up the equation:** Sum of known angles = $165 + 150 + 123 + 100 + 170 = 708$ Sum of unknown angles = $(x + 11) + x = 2x + 11$ Total sum of all angles = $708 + 2x + 11 = 2x + 719$ 4. **Use the formula for the total sum:** $$2x + 719 = 180(7 - 2) = 180 \times 5 = 900$$ 5. **Solve for $x$:** $$2x + 719 = 900$$ $$2x = 900 - 719 = 181$$ $$x = \frac{181}{2} = 90.5$$ 6. **Final answer:** $$x = 90.5$$ This means the two unknown angles are $90.5 + 11 = 101.5$ and $90.5$ degrees respectively.