a square has sum interior angles of 360so for any n gonthe sum of interior angles = 180*(N-2)So we can set up equations:N*135 = 180(n-2)=>135N-180n=-360==> 45n = 360 n = 360/45 = 8similarly, for 156 the n gon is 15, for 162 its 20 gon and for 172.8, its a 50 gon.-n means number of sides so you would basically work backwards180(n-2)/n = 135180n-360/n=135180n-360=135n-55n=-360n= -360/-55 (too lazy to divide it all)do the rest of themthe same way!......
case 2 180n-360 = 156n 180n- 156n= 360 24n = 360 n = 15
case 3 180n -360 = 162 n 180-162n = 360 18n = 360 n = 30
case 4 180n-360 = 172.8n 180n- 360 = 172.8n 180n - 172.8n = 360 7.2n = 360 n = 50
ALL regular n-gons have the interior angles divisible by 180.
this is for a triagle, a square has sum interior angles of 360
so for any n gon the sum of interior angles = 180*(N-2)
So we can set up equations:
N*135 = 180(n-2)=> 135N-180n=-360==> 45n = 360 n = 360/45 = 8
similarly, for 156 the n gon is 15, for 162 it's 20 gon and for 172.8, it's a 50 gon.
