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The number of diagonals in a polygon with n sides is given by n(n-3)/2 (see related question). So, 35 = n(n-3)/2 is what we have to solve. 70 = n(n-3) 70 = n2 - 3n n2 - 3n - 70 = 0 Factorizing the quadratic: (n-10)(n+7) = 0 This gives solutions n = 10 and n = -7. Clearly only the positive answer makes any sense (a shape cannot have minus seven sides!) so our shape has 10 sides: it is a decagon.
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Earn +20 ptsQ: Which polgon has 35 diagonals?
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Continue Learning about Geometry
How many diagonals in decagon?
There are 35 diagonals in a 10 sided decagon
How many diagonals in decagon have?
35
How many diagonals are in a 35 side polygon?
There are 560 diagonals by using the diagonal formula
Does a nonagon have 35 or 27 diagonals?
It has 27.
How many diagonals can you drawn from one vertex in a 35 sided polygon?
In a polygon with n sides, the number of diagonals that can be drawn from one vertex is given by the formula (n-3). Therefore, in a 35-sided polygon, you can draw (35-3) = 32 diagonals from one vertex.
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