### Brain Teasers

# A Regular Series

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?

60, 90, 108, 120, 128.5714, 135, 140, 144, 147.2727, ?

Bonus

What do these numbers represent?

### Hint

Try this angle: divide each number by 180.### Answer

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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