Question

$$ 30 POINTS$$ PLEASE HELP!!!!

David uses drawing software to rotate the regular hexagon about its center. Through which angle measures can he rotate the hexagon to map it onto itself?

Answer 1

60°, 120° and 180° are the angles at which it will map onto itself.

Answer 2

60°, 120°, 180°, 240°, 300° and 360°

Explanation:

We know that 360° is a full rotation and a regular hexagon has 6 angles. So, they will map onto itself every 60°.

`(360)/(6)=60` degrees.

Hence, we will take the multiples of 60 in the range:

`0\leq x\leq 360` degrees

So, we get the following angles:

60°, 120°, 180°, 240°, 300° and 360°.