Math, asked by raynerd212006, 10 months ago

Good Evening Guys

Can anyone send me the steps of this question.

Q.The sum of the exterior angles of a regular polygon is one-ninth the sum of the interior angles. Find the number of sides of the polygon.

Answers

Answered by Anonymous

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good evening dude

Sum of exterior angles of a polygon = 360

sum of interior angle of a polygon = (n - 2) × 180.

therefore, according to the given condition,

360 = [(n-2)×180] ÷ 9

360 × 9 = (n-2)×180

(360 × 9) ÷ 180 = n - 2

2 × 9 = n - 2

18 = n - 2

n = 18 + 2 = 20✅✅✅✅✅

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Answered by Masubi

Let interior angle be x and exterior angle be y

so, x + y = 180°.............(1)

the exterior angle is one-ninth of its interior angle

so, y = x/9.............(2)

substitute (2) in (1)x + x/9 = 180°

(9x + x)/9 = 180°

10x = 180° × 9

x = 18° × 9

x = 162°

so, interior angle is x = 162°

exterior angle is y = 180° - 162° = 18°

so, no. of sides of polygon = 360°/18° = 20

no. of sides of a polygon is 20

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