Question

An exterior angle of a regular convex polygon is 40°. What is the number of sides of the polygon?

A. 8

B. 9

C. 10

D.11

Answer 1

9

Explanation:

Answer 2

option B

Explanation:

Sum of interior angles of a polygon with n sides:

`= (n - 2 )* 180`

`Therefore, Each \ interior \ angle = ((n - 2)/(n) )* 180`

`Sum \ of \ one \ of \ the \ interior \ angle \ with \ its \ exterior \ angle \ is \ 180^\circ`

`[ \ because \ straight \ line \ angle = 180^\circ \ ]`

That is ,

`Exterior \ angle + Interior \ angle = 180^\circ\\\\40^ \circ + ((n-2)/(n)) * 180 = 180^\circ\\\\40 n + 180n - 360 = 180n\\\\40n = 180n - 180n + 360 \\\\40n = 360 \\\\n = 9`

OR

Sum of exterior angles of a regular polygon = 360

Given 1 exterior angle of the regular polygon is 40

Therefore ,

`n * 40 = 360\\\\n = (360)/(40) \\\\n = 9`