Question

if the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have?10122024

Answer 1

Answer:

The polygon has 20 sides.

Skills needed: Polygon Geometry

Step-by-step explanation:

1) We need to first understand what "angle of rotation" is. Angle of rotation essentially is any angle measure that one can rotate a polygon by, but still have the same polygon.

• Example: Square; If you rotate a square by 60 degrees, it will appear slanted, but if you rotate the square by 90 degrees, it will appear exactly like the original shape in terms of orientation.

2) Noticing the pattern: The calculation for the smallest angle of rotation in a regular polygon is $\frac{360}{n}$, with $n$ being the # of sides.

• For a square it is $\frac{360}{4} = 90$, which means 90 is the smallest angle of rotation for this polygon.
• For a pentagon it is $\frac{360}{5} = 72$ degrees.

Formula: $A_r=\frac{360}{n}$ ($A_r = \text{angle of rotation}$, $n=\text{number of sides}$)

3) For this problem, we are given the angle of rotation. We need to find $n$.

$18=\frac{360}{n}$

Multiply by n on both sides: $18n=360$

Divide by 18 on both sides: $n=20$

Therefore, the polygon, which is regular, has 20 sides.

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