Diagonals by Perpendicular Bisector

Geometry Level 2

The perpendicular bisectors of two consecutive sides of a regular polygon form an 18 degrees angle. How many diagonals does this polygon has?


The answer is 170.

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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1 solution

Marta Reece
Dec 26, 2017

Number of vertices is 360 18 = 20 \frac{360}{18}=20

Number of diagonals is n ( n − 3 ) 2 = 170 \frac{n(n-3)}2=\boxed{170}

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