if the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have? 10 12 20 24
If the smallest angle of rotation for a regular polygon is 18°, how many sides does the polygon have? 10, 12, 20, 24
Answer:
To determine the number of sides of a regular polygon given its smallest angle of rotation, we need to understand the relationship between the angle of rotation and the number of sides of the polygon.
For a regular polygon with ( n ) sides, the smallest angle of rotation that maps the polygon onto itself is given by:
\theta = \frac{360^\circ}{n}
Given that the smallest angle of rotation is ( 18^\circ ), we can set up the equation:
\frac{360^\circ}{n} = 18^\circ
To solve for ( n ), we rearrange the equation:
n = \frac{360^\circ}{18^\circ}
Perform the division:
n = 20
Therefore, the regular polygon has \boxed{20} sides.