[Sum of interior and exterior angles of a polygon]

Find the number $n$ of sides of a convex $n$-gon if each of its interior angles is not less than $143^{\circ}$ and not more than $146^{\circ}$.

#
The sum of the interior angles of a convex $n$-gon is $180^{\circ}(n-2)$, therefore
from which we find that $9 \frac{27}{37} \leqslant n \leqslant 10 \frac{20}{27}$. This inequality is satisfied by the unique natural number 10.

## Answer

10.00