A polygon has a sum of all the angles as 1980. How many diagonals will be there in the polygon?
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Answer:
(n - 2) = 1980 / 180 = 11. or, n = 13
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Given : A polygon has a sum of all the angles as 1980°.
To Find : Number of diagonals in the polygon
Solution:
Sum of angles in a polygon of n sides = (n -2) * 180°
(n -2) * 180° = 1980°
=> n - 2 = 11
=> n = 13
Number of sides of polygon = 13
Number of diagonals = n(n - 3) /2
= 13 (13 - 3)/2
= 13 * 5
= 65
There will be 65 diagonals in the polynomial
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