Question

If the outer and inner angles of a regular polygon are in the ratio 2: 3, how many sides does it have?​

Answer 1

Answer:

ratio of exterior angle and interior angle of a regular polygon = 2 : 3

Let exterior angle be 2x and interior angle be 3x.

We know that , each interior angle of a regular polygon = 180° - (exterior angle)

So, 3x = 180° - 2x

5x = 180°

x = 36°,

So, exterior angle = 2*36 = 72°

We know that each exterior angle of a regular polygon = (360/no. of sides of polygon)°

So , 72° = (360/ no.of sides)°

No. Of sides = 360/72 = 5.

Step-by-step explanation:

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