Find the number of diagonals
Geometry
Level
1
An equilateral triangle has no diagonal, a square has 2 diagonals, and a regular pentagon has 5 diagonals.
How many diagonals does a regular 15-sided polygon have?
84
87
90
93
96
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Each vertex can be connected to 1 5 − 3 = 1 2 vertices that are not it and are not next to it. That makes 1 5 ∗ 1 2 = 1 8 0 connections.
But this counts every diagonal twice, once from each direction. So the number needs to be divided by 2. 1 8 0 / 2 = 9 0 .