geometry question.
2006-07-22 16:31:32 · 8 answers · asked by ameliawht 2 in Science & Mathematics ➔ Mathematics
9
because the sides have to be equal if it is a regular polygon and they increase by 180 each time
when u start with 3 it is 180 as each side goes up it goes up by 180 so i found a commond multiple of 162 and 180 it is 1260 and a polygon whose sum is 1260 has nine sides
wow ok i was wrong, way off, everyone else has it right
after seeing everyone had 20 i thought abuot it again and well i was wrong, here's how i come up with 20 now
180(n-2)=162n
180n-360=162n.
18n=360
n=20
o well, no one's perfect!
2006-07-22 16:35:12 · answer #1 · answered by locomexican89 3 · 3⤊ 1⤋
You can also say that the general formula for interior angle of a regular polygon is 180*(n-2)/n, where n is the number of sides of the polygon. So setting this equation equal to 162, and solving for n, you indeed get 20.
2006-07-22 16:50:50 · answer #2 · answered by prune 3 · 0⤊ 0⤋
formula: s = 360/(180 - n ) where s = no. of sides; n = each interior angle value.
s = 360/(180-162)
s = 360/18
s = 20
therefore, the regular polygon with each interior angle measuring 162 degrees is an "ICOSAGON".
2006-07-22 21:33:32 · answer #3 · answered by chan_l_u 2 · 0⤊ 0⤋
You take the difference between the angle you mentioned (162) and 180 (which is a straight line) and divide 360 degrees by it.
360/(180-162)=20
So... a 20 sided one.
2006-07-22 16:50:33 · answer #4 · answered by junvic 2 · 0⤊ 0⤋
the triangle formed by lines from the center would have
two angle of 162/2 = 81 degrees each ...
and 180 - 162 = 18
360 / 18 = 20 ...
a "20-side-o-gon"
2006-07-22 16:39:03 · answer #5 · answered by atheistforthebirthofjesus 6 · 0⤊ 0⤋
20
2006-07-22 16:39:41 · answer #6 · answered by Lindy357 3 · 0⤊ 0⤋
exterior angle will be 180-162=18
no. of sides are 360/18=20
2006-07-22 16:53:24 · answer #7 · answered by mahesh_s11 1 · 0⤊ 0⤋
20
It's an icosagon.
2006-07-22 17:06:48 · answer #8 · answered by Chie 5 · 0⤊ 0⤋