Question

The ratio of n interior angle to the exterior angle of a regular polygon is 5:1 the no of sides of polygon are​

Answer 1

Answer:   12 sided polygon

Step-by-step explanation:   Sum of an interior and its exterior angle is 180 degree .

we have their ratio as 5 : 1 .

Let the common factor be x .

So , interior angle = 5x

exterior angle = x

According to property , we have -

5x + x = 180

6x = 180

So, x = 180 / 6

    x = 30 degree

Hence , each exterior angle = 30 degree ( it is a regular polygon )

Sum of all exterior angles of a polygon = 360 degree

Each side of this polygon = 360 / measure of each exterior angle

                                            = 360 / 30

                                            = 12 sides

Hence , it is a 12 sided polygon .

Thus , this is the answer .