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A An octagon has 20 diagonals
B A hexagon has 9 diagonals
C A hexagon has 4 more diagonals than a pentagon
D A pentagon has the same number of diagonals as it has sides
E A quadrilateral has twice as many diagonals as it has sides
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?