Question

An exterior angle of a regular polygon measures 5degrees. What is the sum of the measures of the interior angles of the regular polygon?

Answer 1

exterior angles of a polygon always add up to 360
and we know that one of the exterior angles=5
we also know that the interior + exterior = 180 degrees

Answer 2

so since you know all exterior angles add up to 360 we can work out what shape we have and how many angles we have inside of the shape

\[\frac{ 360 }{ x }=5\]

Answer 3

72?

Answer 4

yes

Answer 5

Where do I go from there?

Answer 6

okay so it is a 72 sided shape

Answer 7

we know the exterior angle + interior angle = 180

so 180-5= interior angle

Answer 8

then multiply this by 72

Answer 9

175?

Answer 10

and that gives you the sum of interior angles

Answer 11

yes 175
now multiply by 72

Answer 12

14 okay I got it, thank you!!

Answer 13

Whoops not 14, 12600

Answer 14

lmao i didn't do the sum on a calculator but it is a big number so i assume you can use a calculator xD

Answer 15

Yes! (: