Question

how many diagonals can be drawn from each vertex of a heptagon?
______ diagonals per vertex

question 8
1 pts
how many diagonals can be drawn from each vertex of an undecagon?
______ diagonals per vertex

Explanation:

Step1: Recall the formula for diagonals from a vertex

The formula for the number of diagonals that can be drawn from a single vertex of an \(n -\)sided polygon is \(n - 3\). This is because a vertex cannot form a diagonal with itself (\(1\) non - diagonal) and cannot form a diagonal with its two adjacent vertices (\(2\) non - diagonals). So in total, \(1 + 2=3\) non - diagonals from a vertex.

Step2: Calculate for a heptagon

A heptagon has \(n = 7\) sides. Using the formula \(n-3\), we substitute \(n = 7\). So the number of diagonals from a vertex of a heptagon is \(7 - 3=4\).

Step3: Calculate for an undecagon

An undecagon has \(n = 11\) sides. Using the formula \(n - 3\), we substitute \(n=11\). So the number of diagonals from a vertex of an undecagon is \(11 - 3 = 8\).

Answer:

For the heptagon: \(4\)
For the undecagon: \(8\)