A regular polygon has angles of size 150 degrees each. How many sides has the polygon?

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Answer 1 · 2018-06-03T12:43:13

#color(blue)(12)#

The sum of the interior angles of a regular polygon is given by:

#180^@n-360#

Where #bbn# is the number of sides.

Lets call the sum #S#

Then:

#180^@n-360=S \ \ \ \[1]#

If the sum of interior angles is S, then each angle is:

#S/n#

We are given #150^@# for each angles. So,

#S/n=150^@ \ \ \ [2]#

From #[2]#

#S=150n#

Substituting in #[1]#

#180n-360=150n#

#30n=360=>n=12#

The polygon has 12 sides.