Question

interior and exterior angle of a regular polygon is 8 ratio 1 find the number of sides of the regular polygon and each exterior angle of the polygon

Answer 1

let the interior and exterior angles be 8x and 1x respectively
we know, Sun of interior and exterior angle = 360
therefore, 8x + 1x = 360
or 9x= 360
or x= 360/9
or x= 40
therefore
interior angle = 8x = 8×40=320
exterior angle = 1x=1×40=40
since the sum of all exterior angles is 360
therefore we have to divide 360 by 40 to find the no. of sides
360/40= 9
hence this regular polygon have 9 sides.

Answer 2

Answer:9

Step-by-step explanation:

let the interior and exterior angles be 8x and 1x respectively

we know, Sun of interior and exterior angle = 360

therefore, 8x + 1x = 360

or 9x= 360

or x= 360/9

or x= 40

therefore

interior angle = 8x = 8×40=320

exterior angle = 1x=1×40=40

since the sum of all exterior angles is 360

therefore we have to divide 360 by 40 to find the no. of sides

360/40= 9

hence this regular polygon have 9 sides