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

Answer:

option B

Step-by-step explanation:

Sum of interior angles of a polygon with n sides:

                                                                          $= (n - 2 )\times 180$

$Therefore, Each \ interior \ angle = (\frac{n - 2}{n} )\times 180$

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

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

That is ,

$Exterior \ angle + Interior \ angle = 180^\circ\\\\40^ \circ + (\frac{n-2}{n}) \times 180 = 180^\circ\\\\40 n + 180n - 360 = 180n\\\\40n = 180n - 180n + 360 \\\\40n = 360 \\\\n = 9$

OR

Sum of exterior angles of a regular polygon = 360

Given 1 exterior angle of the regular polygon is  40

Therefore ,

               $n \times 40 = 360\\\\n = \frac{360}{40} \\\\n = 9$