Question

The interior angles of a nanogon are in AP. The common difference between those angle is 5 degree. Find the measure of smallest angle.

Answer 1

let the smallest angle be p°

ATQ,

p+(p+5)+(p+5+5)+.....=(9-2)x180

=>these values form an AP, with a=p,d=5°

also,. n,no.of terms=9

so, using the formula , Sn = n/2(2a+(n-1)d)

we get, p=120°

Answer 2

Sn = (n-2)×180
n/2(2a + (n-1)×d) = 7×18o

here n= 9 and d = 5
so, 9/2 (2a + 8d) = 1260
2a+8d = 1260×2÷9
2a+8d = 280
2a+8×5 = 280
2a+ 40 = 280
2a = 280-40
2a = 240
a = 120
smallest angle