Question

By drawing every diagonal from one vertex in a convex, n-sided polygon, the polygon can be decomposed into ___ triangles.

Answer 1

By drawing every diagonal from one vertex in a convex, n-sided polygon, the polygon can be decomposed into (n - 2) triangles.

By drawing every diagonal from one vertex in a convex, n-sided polygon, the polygon can be decomposed into (n - 2) triangles.

Let's consider a convex polygon with n sides. We start by choosing one vertex as our starting point.

From this vertex, we can draw diagonals to all other vertices except for the adjacent ones.

Each diagonal divides the polygon into two smaller polygons.

Since we can draw diagonals to n-3 vertices (excluding adjacent vertices and the starting vertex), the polygon will be decomposed into n-2 triangles.