In a polygon, no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon is $ 70 $, then the number of diagonals of the polygon is

Question

In a polygon, no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon is $ 70 $, then the number of diagonals of the polygon is, $ 20 $, $ 28 $, $ 8 $, $ 7 $

MARKS App · Accepted Answer

A selection of 4 vertices of the polygon gives an intersection of two diagonals. Let the number of sides be n . ⇒ C 4 n = 70 ⇒ n n - 1 n - 2 n - 3 = 24 × 70 = 8 × 7 × 6 × 5 ∴ n = 8 . ∴ The number of diagonals = C 2 8 - 8 = 20 .

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