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

Explanation:

Step1: Recall the formula for diagonals from a vertex

The number of diagonals from a single vertex of an $n$-sided polygon is $n - 3$. This is because we cannot draw a diagonal to the vertex itself and to its two adjacent vertices.

Step2: Identify $n$ for 21 - gon

For a 21 - gon, $n=21$.

Step3: Calculate the number of diagonals

Substitute $n = 21$ into the formula $n - 3$. So, $21-3=18$.

Answer:

18