Question

Square GHIJ shares a common center with regular hexagon ABCDEF on a coordinate plane. AB¯¯¯¯¯ is parallel to GH¯¯¯¯¯. If the combined figure rotates clockwise about its center, at which angle of rotation will the image coincide with the preimage?

60°

180°

90°

240°

Answer 1

Option B 180° is the right answer.

Explanation:

Given is : GHIJ is a square and ABCDEF is a regular hexagon having common centre O.

We know that a square is symmetric at a rotational angle of 90°.

A regular hexagon is symmetric at a rotational angle of 60°.

We will find the LCM of 90 and 60, to know how much to rotate, to get a preimage.

Moreover, a hexagon needs to rotate 180 degrees to coincide with itself.

LCM(60°,90°)=180°.

So, the correct option is B. 180°.

Answer 2

a square needs to rotate 90 to coincide with itself

but the hexagon would need to rotate 180

the answer is 180 degrees