1. **Stating the problem:** We have a convex polygon where the sum of all interior angles except one is 2200⁰. We need to find the excluded interior angle. 2. **Formula for sum of interior angles:** The sum of interior angles of an $n$-sided polygon is given by: $$\text{Sum} = (n-2) \times 180^\circ$$ 3. **Important rule:** Since the polygon is convex, all interior angles are less than 180⁰. 4. **Find the number of sides $n$:** Let the excluded angle be $x$. Then, $$\text{Sum of all angles} = 2200^\circ + x = (n-2) \times 180^\circ$$ 5. We need to find $n$ such that $2200 + x = (n-2) \times 180$ and $x$ is one of the given options. 6. Try each option for $x$: - For $x=140^\circ$: $$2200 + 140 = 2340 = (n-2) \times 180$$ $$n-2 = \frac{2340}{180} = 13$$ $$n = 15$$ 7. Check if $n=15$ is an integer number of sides, which is valid. 8. **Answer:** The excluded interior angle is $\boxed{140^\circ}$. --- **Second problem:** Identify the number of terms in the algebraic expressions: - $3x^2 - x + 9$ has 3 terms. - $4x^3 + x^2 + 3x - 1$ has 4 terms. **Answer:** 3 and 4 --- **Third problem:** Evaluate the expression: $$(-5)^2 \times \left(-\frac{1}{5}\right)^3 - 2^3 \div \left(-\frac{1}{2}\right)^2 - (-1)^{1999}$$ 1. Calculate each part: $$(-5)^2 = 25$$ $$\left(-\frac{1}{5}\right)^3 = -\frac{1}{125}$$ $$25 \times -\frac{1}{125} = -\frac{25}{125} = -\frac{1}{5}$$ 2. Calculate: $$2^3 = 8$$ $$\left(-\frac{1}{2}\right)^2 = \frac{1}{4}$$ $$8 \div \frac{1}{4} = 8 \times 4 = 32$$ 3. Calculate: $$(-1)^{1999} = -1$$ 4. Combine all: $$-\frac{1}{5} - 32 - (-1) = -\frac{1}{5} - 32 + 1 = -\frac{1}{5} - 31 = -31.2$$ **Answer:** $-31.2$