find the number of sides of a polygon, the sum of whose interior angles is 1620°
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find the number of sides of a polygon, the sum of whose interior angles is 1620°
(Show your solutions)
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Answer:
A rectangle having 4 sides can be divided into 2 triangles. We know sum of interior Angles of a triangle is 180°.
=> Sum of interior angles of rectangle = 2 x 180 = 360°
Similarly, pentagon with 5 sides can be divided into 3 triangles , interior angles totalling 180 x 3 = 540°
Generalising, Polygon of n sides can be divided into (n - 2) triangles with interior angles = (n - 2) x 180°.
In given problem, total of interior angles = 1620°.
If number of sides is assumed to be n, then :
(n - 2) x 180 = 1620°
n - 2 = 1620/180 = 9
n = 9 + 2 = 11
Explanation:
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