Geometry test and above

Question

Suppose every interior angle in a regular polygon is 150∘. What kind of polygon is this? 11-gon quadrilateral pentagon 12 gon?

Answer 1

equilateral triangle has interior angles = 60 degrees each = 180(3-2)/3

square has interior angles = 90 degrees = 180(4-2)/4

regular Pentagon interior angles = 180(5-2)/5 = 180(3/5) = 36(3) = 108

regular n sided polygon has interior angles each = 180(n-2)/n

if the interior angles are 150 degrees each, then 150 = 180(n-2)/n and

150n = 180n-360

30n = 360

n = 360/30 = 12 sided polygon