How many diagonals are there in an octagon?

A)56

B)28

C)20

D)16

E)8

Let's examine ONE vertex in an octagon (an 8-sided polygon)

We can draw 5 diagonal lines from that one vertex


So, each of the 8 vertices can have 5 diagonal lines
So, the total number of diagonal lines = (8)(5) = 40

But wait!!

We have inadvertently counted every diagonal TWICE.
For example, we counted the diagonal from vertex A to vertex B AND we counted the diagonal from vertex B to vertex A

So, to account for this DUPLICATION, we must divide 40 by 2 to get 20

Answer: C

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.

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