Question

An exterior angle and an interior angle of a regular polygon are in the ratio 2:7.Find the number of sides in the polygon.?

Answer 1

Answer:

Step-by-step explanation:

7+2 = 9. 180/9 = 20.

Hence exterior angle is 20*2 = 40 degrees and the interior angle 20*7 = 140.

The number of sides of the regular polygon = 360/40 or 9 sides.

Answer 2

Given:

The exterior angle and interior angle of a regular polygon are in the ratio of 2:7

To find:

The number of sides in the polygon

Solution:

The number of sides in the polygon is 9.

We can find the number by following the process given-

We know that the sum of the interior and exterior angle of a regular polygon is 180°.

The ratio of interior and exterior angle=7:2

So, let the interior angle be 7X and let the exterior angle be 2X.

Now, the sum of these angles=180 °

Putting the values,

7X+2X=180°

9X=180°

X=180/9

X=20°

The interior angle, 7X= 7×20=140°

The exterior angle, 2X=2×20=40°

We know that the measure of an exterior angle of a polygon is 360°/N, where N is the number of sides of the polygon.

So, exterior angle=360°/N

N=360°/40°

N=9

Therefore, the number of sides in the polygon is 9.