Question

The number of sides of a regular polygon whose each
exterior angle measures 45° is​

Answer 1

Answer:

Let n be the number of sides of the polygon.

The sum of the exterior angles of a regular polygon

=

360

∘

45

∘

×

n

=

360

∘

[Since the measure of each exterior angle is

45

∘

]

n

=

360

45

[Simplify]

n

=

8

[Simplify]

The sum of the exterior angles of a regular polygon=360∘45∘×n=360∘[Since the measure of each exterior angle is 45∘]n=36045[Simplify]n=8[Simplify]

Therefore, the number of sides of a regular polygon whose each exterior angle has a measure of

45

∘

45∘ is 8.