Question

the diff bet any two cons interor angles of a polygon is 5 degree.If the smallest angle is 120 degrees,find the no. of sides of polygon

Answer 1

So CONSIDERING smallest angle 120 then next angles turns to be 120+5 then next one 120 +2x5 until lets say N angle 120+N5...

Sum of these angle must be multiple of 180......

Answer 2

siddharth are u sure this is the info... I mean something like smallest polygon or something else info...

Answer 3

i m sure that the ques is complete its given in my book

Answer 4

do u know the answer?

Answer 5

9.

You need to assume the polygon is convex else u could go on for ever.

If you imagine walking around the polygon, then u make a circle of 360 and u turn through successive exterior angles which must sum to that.

60 + 55 + 50 +...for 9 terms gives 360.

Answer 6

9 is correct...plz explain me this cocept of a convex polygon and the way u solved the problem

Answer 7

Convex intuitively means the corners "stick out". If they are allowed to go "in" and then "back out" your polygon could have any number of sides at all (imagine zigzagging all over the page).


The other is what I said above, imagine the (convex) polygon is sitting on the floor and you are standing on one side and looking at the angle of 120 degrees.

The exterior angle there is 60 degrees and if you walk to the corner and turn through 60 degrees you will then start to walk on the second line and so on.

If you think about it, you have to walk in a circle or 360 degrees.

So the sum of all the angles u turn through on your way back to the start is 360 degrees ie 60 + 55 + 50 +.....=360.

Answer 8

i understood this walking thing and the concept that on reaching the point from where we started will mean our path is a circle but the ques is now how can the sum of the turning angles be equal to 360...can u plzzzzzz explain with a figure the ;last part because 360 will be equal to the sum of all the interior angles according to me

Answer 9

The interior angles will be (n-2)* 180 because you can think of the polygon as being put together as (n-2) triangles (draw lines from a vertex to every other vertex).

For the exterior angles, I don't know how to explain it better than I did, just imagine walking around one and think about your body and which way you are facing. At the end of each side, you turn by the exterior angle in order to start walking on the next side.
When you come up to the last, your body has turned a complete circle and is facing the same as when you started.

Answer 10

thnx for d help

Answer 11

Sure, np.

Answer 12

so you mean to say that we keep on turning by some angle to move along the polygon and finally on reaching the same point the sum of all the angular turns will be equal to 360 as we had completed a circular path

Answer 13

wat is n,the no. of sides?

Answer 14

Yes and Yes. Try it for real, draw a triangle on the floor or just arrange some objects a triangle and walk round it.