1. **State the problem:** We have a convex polygon with six interior angles given as: - 131° - $s + 49$° - $2s - 12$° - $3s - 43$° - $s + 44$° - $2s + 20$° We need to find the value of $s$. 2. **Formula used:** The sum of interior angles of a polygon with $n$ sides is given by: $$\text{Sum of interior angles} = (n - 2) \times 180$$ Since there are 6 angles, $n=6$. 3. **Calculate the sum of interior angles:** $$ (6 - 2) \times 180 = 4 \times 180 = 720 $$ 4. **Set up the equation:** Sum of all given angles equals 720: $$131 + (s + 49) + (2s - 12) + (3s - 43) + (s + 44) + (2s + 20) = 720$$ 5. **Simplify the left side:** Combine like terms: $$131 + s + 49 + 2s - 12 + 3s - 43 + s + 44 + 2s + 20 = 720$$ Group $s$ terms: $$s + 2s + 3s + s + 2s = 9s$$ Sum constants: $$131 + 49 - 12 - 43 + 44 + 20 = 189$$ So the equation becomes: $$9s + 189 = 720$$ 6. **Solve for $s$:** Subtract 189 from both sides: $$9s + \cancel{189} - \cancel{189} = 720 - 189$$ $$9s = 531$$ Divide both sides by 9: $$\frac{9s}{\cancel{9}} = \frac{531}{\cancel{9}}$$ $$s = 59$$ **Final answer:** $$\boxed{59}$$