Question

a parallelogram rotates about its center. At what angle of rotation will the image of the parallelogram coincide with its preimage?

a) 30 deg.
b) 90 deg.
c) 180 deg.
d) 270 deg.
e) 315 deg.

Answer 1

The correct answer is option C. i.e. When a a parallelogram rotates about its center., then taking 180 degrees as the angle of rotation, the image of the parallelogram coincide with its preimage. Thus 180 degree rotation is the answer.

Answer 2

The angle of rotation that always will reproduce the preimage is 180°

At what angle of rotation do we get back the preimage?

A parallelogram is a figure where opposite sides are parallel. Particularly, the number of sides must be even, and there is no other restriction.

We know that if we perform a rotation equal to one interior angle of the figure, we get back the original figure, but in this case we talk about parallelograms, so we must be more general about it.

Now, because opposite sides are parallel, if we divide the figure exactly by its half, we will have the exact same thing in both sides. This means that the figure is symmetric.

From that, we conclude that if we do a reflection across that line (which is equivalent to a rotation of 180°) we get the same image.

Then the correct option is C, 180°.

If you want to learn more about rotations:

https://brainly.com/question/4289712

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