Question

A regular hexagon is rotated about its center. Which degree measure will carry the regular hexagon onto itself ?

Answer 1

Answer:

Image result for A regular hexagon is rotated about its center. Which degree measure will carry the regular hexagon onto itself ?

There are 6 angles between neighbor vertices, they all are equal and their sum is 360°

Answer 2

When a shape is rotated, it must be rotated through a point.

The degree measure that will carry the regular hexagon onto itself is 60 degrees

The angle at the center of a regular hexagon is:

$\mathbf{\theta = 360^o}$

The number of sides of a regular hexagon is:

$\mathbf{n = 6}$

So, the degree measure that carries the hexagon onto itself is:

$\mathbf{\alpha = \frac{\theta}{n}}$

Substitute known values

$\mathbf{\alpha = \frac{360^o}{6}}$

$\mathbf{\alpha = 60^o}$

Hence, the degree measure that carries the hexagon onto itself is: 60

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