Question

find the number of sides of regular polygons if the exterior angle is one-ninthof its interior.angle.​

Answer 1

Answer:

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

Step-by-step explanation:

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Answer 2

Answer:

HI FRIEND HERE IS YOUR ANSWER ,

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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