Question

a circle is divided into 10 sectors.the sizes of angles are in ap, the angle of largest sector is seven times angle in small sector. find small sector

Answer 1

so the angles are:
a, a+d, a+2d, ... , a+9d

a+9d = 7a
9d = 6a
d = 2a/3

also sum of the 10 terms = 360
(10/2)(2a + 9d) = 360
2a + 9d = 72
sub in other value:
2a + 9(2a/3) = 72
6a + 18a = 216
a = 9
then d = 18/3 = 6

the angle of the small sector is 9°

check:
terms are 9, 15, 21, .... , 63
the last term is 7 times the first? , Check!
sum of terms = 5(first + last) = 5(9+63) = 360, Check!