Question

The smallest angle of rotational symmetry for a regular polygon is 30°. How many sides does the regular polygon have?

Answer 1

Answer:

Number of sides are 12.

Step-by-step explanation:

Given that smallest angle of rotational symmetry for a regular polygon is 30°.

we have to find the number of sides does the regular polygon have.

If we can rotate a figure around a center point by fewer than 360° and the figure appears unchanged, then the figure has the rotation symmetry.

Now as at the centre the angle is 360 and all the angles at the centre formed equal i.e

$\text{No. of sides= }\frac{360}{\text{smallest angle at centre}}=12$

Hence, 12 number of sides the polygon have.

Answer 2

Answer: Hello there!

If you have an regular poligon of N sides, then the angles of rotational simetrys are of:

A = n*360°/N where n can take the values = 1, 2 ,.....,N

and you have N different angles.

and the smallest rotational simetry is when n is equal to 1.

So A = 360/N

in this case, R = 30°, and we want to find the number N.

30° = 360°/N

N = 360°/30° = 12

This means that te regular polygon has 12 sides.