Question

how many distinct diagonals does an octagon have?
______ diagonals

question 13
how many diagonals can be drawn from each vertex of an octagon?
______ diagonals per vertex

Explanation:

Step1: Recall the formula for the number of diagonals in a polygon

The formula for the number of diagonals \(D\) in an \(n -\)sided polygon is \(D=\frac{n(n - 3)}{2}\). For an octagon, \(n = 8\).

Step2: Calculate the number of diagonals

Substitute \(n=8\) into the formula: \(D=\frac{8\times(8 - 3)}{2}=\frac{8\times5}{2}=20\).

Step3: Recall the formula for the number of diagonals from a single vertex

The formula for the number of diagonals from a single vertex of an \(n -\)sided polygon is \(n-3\). For an octagon (\(n = 8\)), the number of diagonals from a single vertex is \(8 - 3=5\).

Answer:

20 diagonals
5 diagonals per vertex