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

Explanation:

Step1: Recall diagonal - vertex relationship

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 an octagon

An octagon has $n=8$ sides.

Step3: Calculate the number of diagonals

Substitute $n = 8$ into the formula $n - 3$. We get $8-3=5$.

Answer:

5