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The sum of the exterior angles of any polygon is 360o. For a regular polygon, they are all the same, so 360o divided by the size of exterior angleo will give you how many sides the polygon has.

The interior and exterior angles of a polygon are supplementary and so sum to 180o.

So given the internal angle, subtract from 180o and then divide into 360o and you will have the number of sides.

  • Interior angle = 144o
exterior angle = 180o - 144o = 36o.

number of sides = 360o / 36o = 10 (a decagon).

  • Interior angle = 140o
Left as an exercise for the reader.

reader:

ext.a.=180-140=40

n. of s.=360/40=9

Thanks a lot!

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Q: Find the number of sides of a regular polygon with an internal angle of size a.144 b. 140?
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