Question 1
Let $P_1P_2\ldots P_{2021}$ be a convex polygon with 2021 vertices such that, at every vertex $P_i$, the 2018 diagonals from $P_i$ divide the angle $\widehat P_i$ into 2019 equal angles.
Prove that $P_1P_2\ldots P_{2021}$ is a regular polygon, that is, all its angles have the same measure and all its sides have the same length.
Prove that $P_1P_2\ldots P_{2021}$ is a regular polygon, that is, all its angles have the same measure and all its sides have the same length.