Question

a. the number of diagonals that intersect at a given vertex of a triangle is 0. b. the number of diagonals that intersect at a given vertex of an octagon is 5. c. the number of diagonals that intersect at a given vertex of a 21 - gon is 18. d. the number of diagonals that intersect at a given vertex of an n - gon is

Explanation:

Step1: Understand diagonal - vertex relationship

For a polygon with $n$ sides, we cannot draw a diagonal to the vertex itself and to its two adjacent vertices.

Step2: Derive the formula

The number of diagonals from a single vertex of an $n$-gon is $n - 3$.

Answer:

$n - 3$