If the individual measure of an angle in a regular polygon is #156°# how many sides does the polygon have?

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Answer 1 · 2018-06-08T11:58:33

#15#

The sum of the internal angles of a polygon with #n# sides is #(n-2) * 180# degrees.

If the polygon is regular, all the angles have the same measure, which means that each angle is

#\frac{(n-2) * 180}{n}# degrees.

We know that this equals #156#, so we have

#\frac{(n-2) * 180}{n} = 156#

Multiply both sides by #n#:

#(n-2) * 180 = 180n - 360= 156n#

Subtract #156n# from and add #360# to both sides

#180n-156n = 24n= 360#

Divide both sides by #24#:

#n = \frac{360}{24} = 15#

Answer 2 · 2018-06-08T12:33:37

#15# sides

The sum of the exterior angles of any polygon is always 360°.

You can calculate the number of sides from #(360°)/("ext angle")#

Ext angle = #180°-156° = 24°#

#360/24 = 15# sides