From a vertex of a n-sided convex polygon we draw the diagonals. I want to show that the angles that are created between two consecutive diagonals are all equal.
For that do we have to consider the triangles that created and to show that these have the angles?
For a regular $n$-gon with vertices $P_1,\ldots,P_n$ in order, we have $\angle P_k P_1 P_{k+1}=\pi/n$ for $2\le k\le n-1$.
To see this, consider the circumcircle $O$ and use the fact that the angle subtended by an arc at a point on $O$ is a half of the angle subtended at the centre of $O$.