what sector has the greatest angle
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Step-by-step explanation:
major sector has the greater angle...
Answered by
2
Answer:
circle is completely divided into n sectors in such a way that the angles of the sectors are in AP. if the smallest of these angles is 8
o
and the largest is 72
o
then the angle in the fifth sector is ?
Step-by-step explanation:
Let the common difference be d.
Let T
r
denote the angle of the r
th
sector.
Using AP formula:
T
r
=8+(r−1)d
72=8+(n−1)d
⟹(n−1)d=64 (1)
Sum of all angles: 360
o
Sum of first n terms of AP is given by:
2
n
(2a+(n−1)d)
2
n
(16+64)=360
⟹n(40)=360⟹n=9
Substituing n=9 in (1):
d=8
Therefore, angle of fifth sector = T
5
=8+4⋅8=
40
o
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