What type of polygon has an interior angle sum of 6840°?

The sum of interior angles formula is:

S = 180(n - 2)

In this case:

6840 = 180(n - 2)

Let's solve for n:

Divide both sides by 180:

38 = n - 2

Add 2:

n = 40

Therefore, this polygon is a 40-gon. If you want to be super cool, you could call it a tetracontagon.