Question

3. The exterior angle of a regular polygon is one-fifth of its interior angle. How many sides have the
Is 1089. Find the number of sides of the polye
2.
polygon?
d the measure of​

Answer 1

Let interior angle be x,

Exterior angle = x/5

formula of sides

(360° / exterior angle ),

(360° / 180-interior angle)

360°/(x/5) =360° /(180°- x)

x / 5 = 180° -x

6x/5 = 180°

x = 180° × 5/6 = 150°

Interior angle = 150°

THEREFORE,

Sides = 360° / 180° - 150° = 360° / 30° = 12 sides .

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