Question

(a) Find the sum of angles of a polygon with 22 sides (b) The sum of angles of a polygon is 81000 .Find the number of its sides​

Answer 1

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a) The sum of the exterior angles of any n-gon is 360˚. Find the sum of the interior angles of a 22-gon.

Since the polygon has 22 sides, we can substitute this number for n: (n 2)180˚= (22 2)180˚= 20180˚= 3600˚. Each angle of a regular polygon measures 157.5˚.

b) Given: Sum of the angles = 8100°

Sum of the angles of n-sided polygon = (n – 2) × 180°

⇒ 8100° = (n – 2) × 180°

⇒ 8100/100 = n - 2

⇒ 45 = n – 2

⇒ n = 45 + 2

⇒ n = 47

∴ The number of sides of polygon having sum of the angles of 8100° is 47 sides.

$\sf{{Hope \: it\: }{helps \: you}}$

Answer 2

a) 3600°

b) 47

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