Question

the sum of the interior angles of a polygon is 4 times the sum of its exterior angle find the number of sides in a polygon

Answer 1

Sum of the exterior angles of a regular polygon is 4 times the sum of its exterior angles =360∘ ∴ Sum of interior angles =4×360∘ Again we have sum of interior angles s=(n−2)180∘ Where n is the number of sides of the polygon (n−2)180∘=  1440[degree]
n-2=8
n=8+2=10
so,10 is the correct answer

Answer 2

Answer:

10

Step-by-step explanation:

The sum of the interior angle =4 times the sum of the exterior angles.

Therefore, the sum of the interior angles =4×360°=1440.

=(n-2)×180°= 1440°

=(n-2) =1440/180

=8

=n =8+2

=10.