The interior angles of a convex polygon are in AP. If the largest angle is 140, and the smallest is 100, then the number of sides of the polygon is?
6, 8, 10, 11 or 12

Question

The interior angles of a convex polygon are in AP. If the largest angle is 140, and the smallest is 100, then the number of sides of the polygon is?
6, 8, 10, 11 or 12

crashonce · Answer

@ikram002p

crashonce · Answer

@ganeshie8

crashonce · Answer

@jim_thompson5910

crashonce · Answer

@Compassionate

ganeshie8 · Answer

$$100 + (n-1)d = 140$$

$$(n-1)d = 40$$

crashonce · Answer

not sure

ikram002p · Answer

i might confsed u xD
i remove my comments and read carfully what ganesh wrote

crashonce · Answer

so its 11?

ganeshie8 · Answer

Also the interior angles must add up to :  $180(n-2)$

ganeshie8 · Answer

So you have two equations basically :

$$(n-1)d = 40\tag{1}$$
$$\frac{n}{2}\left[2\times 100 + (n-1)d\right] = 180(n-2)\tag{2}$$

ganeshie8 · Answer

you can solve them http://www.wolframalpha.com/input/?i=solve+%28n-1%29d+%3D+40%2C%5Cfrac%7Bn%7D%7B2%7D%5Cleft%5B2%5Ctimes+100+%2B+%28n-1%29d%5Cright%5D+%3D+180%28n-2%29

crashonce · Answer

wait is it 6 or 8

ganeshie8 · Answer

you have two equations and two unknowns, you can solve them right ?

crashonce · Answer

ooooo its 6 right? sorry

ganeshie8 · Answer

yes let me knw if something doesnt make sense..

crashonce · Answer

it makes sense
i gott another one

ganeshie8 · Answer

we have used "nth term" and the "partial sum" formulas of AP