Question

the ratio of interior to exterior angle of a regular polygon is 7:2.Find the number of sides of polygon.

Answer 1

Ext=2x
Int=7x
Int+ext=180
2x+7x=180
9x=180
x=20
Ext=2×20=40

No of sides =360/40
=9 sides.

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Answer 2

Ratio between interior and exterior angle = 7 : 2

Let the interior angle be 7x and the exterior angle be 2x.

As we know that any interior and exterior angle on same vertex of a polygon makes a straight line and which implies that their sum is 180 degrees.

So,

7x + 2x = 180

9x = 180

x = 180/9

x = 20 degrees

Hence,

Exterior angle = 2x = 2 * 20 = 40 degrees

Since it is a regular polygon so all the exterior angles will be equal to each other and all the interior angles will be equal to each other as well.

So,

Number of sides of the polygon = 360/Each exterior angle

Number of sides = 360/40 = 36/4 = 9

Hence this polygon has 9 sides.

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