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## A Regular Series

Series teasers are where you try to complete the sequence of a series of letters, numbers or objects.

 Puzzle ID: #30476 Fun: (2.7) Difficulty: (2.69) Category: Series Submitted By: MarcM1098 Corrected By: MarcM1098

What number comes next in this series? The decimals are rounded to 4 places.
60, 90, 108, 120, 128.5714, 135, 140, 144, 147.2727, ?

Bonus
What do these numbers represent?

The next number is 150.
The formula is 180(n-2)/n, starting with n=3 for the first term.
180*1/3=60
180*2/4=90
180*3/5=108
180*4/6=120
...
180*10/12=150

Bonus
These numbers are the size (in degrees) of the interior angles in a regular n-sided polygon. An equilateral triangle has three 60 degree angles, a square has four 90 degree angles, a regular pentagon has five 108 degree angles, and so on. A regular dodecagon has twelve 150 degree angles.

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