A circle is completely divided into to n sectors in such a way that the angles of the sectors are inAP. If the smallest of these angles is `8^(@)`and the largest is `72^(@)`, calculate n and the angle in the fifth sector.

A circle is completely divided into to n sectors in such a way that th

1.	A circle is completely divided into to n sectors in such a way that the angles of the sectors are inAP. If the smallest of these angles is `8^(@)`and the largest is `72^(@)`, calculate n and the angle in the fifth sector.
Answer» Correct Answer - n=9,5th angle = `40^(@)` Let the number of sectors be n. Then, ` n/2 (a+l) = 360 Rightarrow n(8 +72) = 720 Rightarrow n = 720/80 =9` Now, a=8` T_(n) = 72 and n=9` 8+8d = 72 ` Rightarrow 8d=64 Rightarrow d=8` So, the AP is 8,16,24,32,….., So,5th angle = (a+4d) ` 40^(@)`