Make and test a conjecture about the number of diagonals of a pentagon. Write a conjecture for the general case.

The correct answer is: 6(6 - 3)/2 = 9

We will consider a pentagon

We observe that there are 5 diagonals in a pentagon.
Now, for an “n” sided-polygon, the number of diagonals can be obtained by the following formula:
Number of Diagonals = n(n-3)/2
This formula is simply formed by the combination of diagonals that each vertex sends to another vertex and then subtracting the total sides. In other words, an n-sided polygon has n-vertices which can be joined with each other in ⁿC₂  ways.
Now by subtracting n with ⁿC₂
ways, the formula obtained is

n(n-3)/2.
For example, in a hexagon, the total sides are 6.
So, the total diagonals will be 6(6-3)/2 = 9.