### 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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## Comments

wow...tough one! Thanks.

Not too tough, but wouldn't have thought about the bonus at all. Obvious when you mention it though.

Nice one! Really fresh view on the series for a change!

it was obvious... I got both the series and also the bonus answer

Got this one! Not an easy one though, but possible to solve if one has a mathematical bent of mind!

Didn't get it, but was ont he right track, and I noticed the curious interior angles, as 108 for whatever jumped out, but I didn't put it all together. Nicely done

Cool teaser.

Surprised at how quickly I got it...something about 90-108-120 just clicked.

Surprised at how quickly I got it...something about 90-108-120 just clicked.

Nice teaser!

I got it as soon as I saw the hint. All those memory from the high school came back to me! I really enjoyed. Thanks.

I got it as soon as I saw the hint. All those memory from the high school came back to me! I really enjoyed. Thanks.

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