Asked by Anonymous
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
Answers
Answered by
Reiny
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!
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!