Question

Is there a ploygon which has only 2 types of interior angles 120 & 60 degree? Is so how many sides such a polygon has ?

Answer 1

120*2 + 60*2 = 240 + 120 = 360
so a quadrilateral is possible ?

there can be many other polygons, just setup equations and solve them

Answer 2

But y to multiply 2 ?

Answer 3

120*2 + 60*2

this expression tells,
i hav picked a polygon wid two 120 angles, and two 60 angles

Answer 4

^^ above quadrilateral, i see oly two type of angles : 60 and 120

Answer 5

thank u

Answer 6

np :)

Answer 7

120*2 + 60*2 = 240 + 120 = 360
so a quadrilateral is possible
Can we solve only this much ?

Answer 8

question is asking us, if a polygon is possible.
we showed that a quadrilateral is possible. so we're done.

ofcourse we can pursue analyzing wat all kinds of polygons are possible...

Answer 9

Is so how many sides such a polygon has ?

Answer 10

Sorry that was little mistaken this is the actual question
Is there a ploygon which has only 2 types of interior angles 120 & 60 degree? Is so how many sides such a polygon has ?

Please solve it completely sir .I am completely confused ?

Answer 11

here is the equation to solve :-

60x + 120y = 180(n-2)

you need to solve x, y, and n in positive integers

n = x+y

Answer 12

60x + 120y = 180(n-2)

x+ 2y = 3(n-2)

x+2y = 3(x+y-2)

simplify

Answer 13

Hint :-If n is the no of sides & if k angles are of 60 degree,then n-k angles are of 120 degree and (n-2)180=60k+120(n-k)

Answer 14

did u get my previous reply ?

Answer 15

Really no

Answer 16

60x + 120y = 180(n-2)

x+ 2y = 3(n-2)

x+2y = 3(x+y-2)

x + 2y = 3x + 3y - 6

2x + y = 6

Answer 17

so, the possible positive values for x, y are :-

x = 0, y = 6 (hexagon)
x = 1, y = 4 (pentagon)
x = 2, y = 2 (quadrilateral)
x = 3, y = 0 (triangle)

Answer 18

answer is 4 or 5.
But teach me that how to solve that ?

Answer 19

answer is 4 or 5,
if we want both types of angles to exist in our polygon - as can be seen in above table.

Answer 20

go thru the above posts, let it sink a bit.... and then come back if u still get stuck :)

Answer 21

I am really happy because i really got ot by u..
THANK U

Answer 22

Sure ?

Answer 23

how n=x+y

Answer 24

good question :)
msg me when you're online

Answer 25

ok