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### Theory:

Adjacent vertices: The end-points of the same side of a polygon are called the adjacent vertices.

Adjacent sides: Sides of a polygon that have a common vertex are called adjacent sides. If the sides of a polygon don't have any common vertex is called non-adjacent sides.
Example:
Consider a quadrilateral $$ABCD$$.

Here, the vertex $$A$$ adjacent to vertex $$B$$ in the side $$AB$$ and adjacent to vertex $$C$$ in the side $$AC$$. Thus, the vertex $$A$$ is adjacent to the vertex $$B$$ as well as the vertex $$C$$. But the vertex $$A$$ is non-adjacent to the vertex $$D$$.

Also, the side $$AB$$ is adjacent to side $$BD$$ when we consider the common vertex as $$B$$, and it is adjacent to the side $$AC$$ when we consider the common vertex as $$A$$. But the side $$AB$$ is non-adjacent to the side $$AD$$.
Important!
• Convex polygons have no portions of their diagonals in their exterior which is not true in case of concave polygons.
• For each vertex of a polygon, there are two adjacent vertices and remaining are non-adjacent vertices. Thus, in $$n$$-gon, there are '$$n-2$$' non-adjacent vertices for a vertex.
• For each side of a polygon, there are two adjacent sides, and the remaining are non-adjacent sides. Thus, in $$n$$-gon, there are '$$n-2$$' non-adjacent sides for each side.
• Diagonals: The line segments obtained by joining vertices which are not adjacent are called the diagonals of a polygon.
The number of diagonals of a convex polygon:  If there are $$n$$-sides in a convex polygon and $$n > 3$$, then it has $\frac{n\left(n-3\right)}{2}$ diagonals. A triangle has no diagonals.
Example:
Consider a $$16$$-gon.

Let's find the number of diagonals in it.

We have the number of sides $$n = 16$$.

Substitute the value in the formula.
The number of diagonals in $$16$$-gon $$=$$$\frac{16\left(16-3\right)}{2}$ $$= 104$$.
Important!
In a triangle, all the sides/vertices are adjacent to each other. Therefore, we cannot draw diagonals in it. Thus, the number of diagonals in any triangle is $$0$$.