3 600° ÷ 180° = 20 sides
20 sides + 2 sides = 22 sides
The polygon is a perfect dodecagon (12 sides)
Simply divide 132 units by 11 units to get the number of sides. The question did not mention any variance to the lengths of the polygons, so it is assumed that each side has the same length.
Always remember that there is a total sum of 360° of every exterior angle beside an interior angle. This is only applies to regular polygon, a polygon that has exactly same interior angle for each included angle. We should also always know that the side of a polygon is also the amount of how many interior angles or how many exterior angle it has.
Since there is 165° angle for each interior angle. The exterior of the angle beside it is 180°-165°=15° which is also called the supplementary angle.
We already know that there are 360° of total sum of the exterior angle that a polygon has, and the polygon that we are talking about has a 15° amount of exterior angle so we need to know how many 15° it is needed for us to acquire 360° be dividing so 360°/15° which is equal to 24, the amount of exterior angle that the polygon we are talking about. Hence, a regular polygon that has an interior angle of 165° has a total side of 24.
A polygon has three sides.
Number of sides is 12.
Sum of interior angle and exterior angle of a polygon is 180 degree.
Let exterior angle is x.
Interior angle is 5x.
x + 5x = 180°
Sum of all exterior angles of a polygon is 360 degree
So n X x = 360°
n = 360°/30°
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