016. A circle is completely divided into n sectors in such a way that

1.	016. A circle is completely divided into n sectors in such a way that the angles of the sectorsare in arithmetic progression. If the smallest-of these angles is 8 and the largest 72calculate n and the angle in the fourth sector.
Answer» First angle, a = 8°nth angle, an = 72°let the common difference = d sum of angles = 360°⇒ (n/2)[a + an] = 360⇒(n/2)[8+72] = 360⇒(n/2)[80] = 360⇒ 40n = 360⇒ n = 360/40⇒ n = 9 72 = 8+(n-1)d⇒ 72 - 8= (9-1)d⇒ 64 = 8d⇒ d = 64/8⇒ d = 8° a₃ = a + (n-1)d⇒a₃ = 8 + (4-1)×8⇒a₃ = 32 n = 9angle of fourth sector = 32°

016. A circle is completely divided into n sectors in such a way that the angles of the sectorsare in arithmetic progression. If the smallest-of these angles is 8 and the largest 72calculate n and the angle in the fourth sector.

Answer»

First angle, a = 8°nth angle, an = 72°let the common difference = d

sum of angles = 360°⇒ (n/2)[a + an] = 360⇒(n/2)[8+72] = 360⇒(n/2)[80] = 360⇒ 40n = 360⇒ n = 360/40⇒ n = 9

72 = 8+(n-1)d⇒ 72 - 8= (9-1)d⇒ 64 = 8d⇒ d = 64/8⇒ d = 8°

a₃ = a + (n-1)d⇒a₃ = 8 + (4-1)×8⇒a₃ = 32

n = 9angle of fourth sector = 32°