Question

The interior angles of a convex polygon are in AP. The smallest angle is 120 & the common difference is 5. Find the number of sides of the polygon - A10 In

11th - 12th Class

Maths

Solution

128

4.0 (1 ratings)

( P_{n}=frac{n}{2}[2 a+(n-1) d]=(n-2)(pi) ) ( frac{n}{2}[240+(n-1) 5]=(n-2)(1801 ) ( 3-120 n+5 frac{n^{2}}{2}-frac{5 n}{2}=180 n-360 ) ( -380+frac{5 n^{2}}{2}=55 n ) ( -255 n^{2}-130 n+720=0 ) ( n=8,18 )