The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector has a central angle of 66°, what fraction of the wheel’s area is represented by the smallest sector?	Select
A) 1/24
B) 1/20
C) 1/15
D) 1/12
E) 1/10
The largest angle is 66.   Let d be the difference between any two angles in the progression.   The sum of all the angles will be:   66 + (66-d) + (66-2d) + ... + (66-7d) = 528 - 28d   The sum of all the central angles in a circle = 360   528 - 28d = 360   d = 168/28= 
<gadget id="calculator">168/28</gadget>
<output>6</output>
6   The smallest sector is (66-7d)= 66-7*6= 
<gadget id="calculator">66-7*6</gadget>
<output>24</output>
24   The fraction of the area covered is 24/360= 1/15.   The answer is 1/15.
<result>C</result>
The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector has a central angle of 66°, what fraction of the wheel’s area is represented by the smallest sector?