Question

In a polygon 5 angles are 172° and remaining are 160° find no. of sides

Answer 1

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Let no. of sides be n.
Now,
Sum of 5 interior angles = 5 * 172 = 860°
Sum of other angles =  860 + (n-5)*160    [∵ 5 int. ∠s = 860°]
⇒ (n-2) * 180 = 860 + (n-5) * 160
⇒ 180n - 360 = 860 + 160n - 800
⇒ 20n = 420
⇒ n = 21

Hence no. of sides = 21.

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