Question

Find the number of sides of a convex polygon if the measures of its interior angles have a sum of 12,600 degrees

Answer 1

sum of external angles = 360
so each ext angle = 360/n
and interior angle = 180 - (360/n) where n = no. of sides
so n ( 180 - 360/n) = 12600
solve this for n

Answer 2

solving
180n - 360 = 12600
180n = 12960
n = 12960/180 = 72 sides

Answer 3

ok?

Answer 4

How did you know what formula to use?

Answer 5

i started from the fact that sum of external angles = 360 degrees
perhaps a drawing will help

Answer 6

the 6 exterior angles e add up to 360 degrees so each ext angles = 60 degrees
an interior angle i is 180 - e = 120
so total angles in the figure = 6 * 120 = 720

Answer 7

Okay, now I understand. Thank you

Answer 8

there is a formula for the total number od degrees is polygon of no. sides = n
it is

total degrees = 180(n - 2)
so here

12600 = 180( n - 2)
solve for n

Answer 9

12600 = 180n - 360
180n = -12600 - 360
180n = 12960
n = 72

Answer 10

yep

Answer 11

i forget that formula for some reason ! - its easier using that