Question

The ratio of exterior angle to interior angle of a regular polygon is 1:4.Find the number of sides of the polygon. ​

Answer 1

Answer:

Step-by-step explanation:

Let the interior angle of the regular polygon be x.

Therefore, the exterior angle is x/4.

Exterior angle + adjacent interior angle = 180°

x/4 + x. = 180°

5x /4. = 180°

x. = 180° * 4/5

= 144°

The interior angle is 144°.

The exterior angle is 36°.

Let n be the number of sides.

n = 360°/ exterior angle

= 360° / 36°

= 10

Ans.= The number of sides of a regular polygon is 10.

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Answer 2

let the exterior angle be x and interior angle be 4x

exterior angle + interior angle = 180 (supplementary angles)

⇒ x + 4x = 180

⇒ 5x = 180

⇒ x = 180/5

∴ x = 36°

4x = 4*36° = 144°

exterior angle of a polygon = 360/no. of sides of the polygon

∴ no. of sides of the polygon = 360/exterior angle = 360/36 = 10 sides

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