Question

The sum of the outer angles of polygon is twice the
sum of the inner angles. How many sides does it have?
What if the sum of outer angles is half the sum of inner
angles? And if the sums are equal?​

Answer 1

Step-by-step explanation:

Sum of interior angles of a polygon =(n−2)∗180

∘

Sum of exterior angles of a regular polygon =360

∘

2(n−2)∗180

∘

=360

∘

n−2=1⇒n=3

(ii) 360

∘

=

2

1

(n−2)180

∘

n−2=4⇒n=6

(iii)(n−2)∗180

∘

=360

∘

n−2=2⇒n=4