Question

The ratio between interior and exterior angle of a regular polygon is 1 : 8.
Find the number of sides of the polygon.

Answer 1

Answer:

18 sides

Step-by-step explanation:

1 : 8 = 9 ( x + 8x =9x )

9x = 180

x = 180 / 9 == 20

exterior angle 20°

interior angle 8 × 20 = 160

sides of polygons = sum of exterior angle / exterior angle

360 / 20 = 18 sides

Answer 2

Let consider the interior angle of the regular polygon be X.

∴ the exterior angle is X/8.

Exterior angle + adjacent interior angle =180°

$\frac{x}{8}$+X=180°

9X/8​=180°

X=180°×8/9

X= 20°×8= 160°

the interior angle is 160°

the exterior angle is= ( 180° - 160°) = 20°

n=360°​ ÷exterior angle

=360°÷20° =18

Hence the number of sides of a regular polygon is 18.

Ans :- Number of sides of the polygon is 18.

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