Angle WXY underwent a sequence of two rotations around different centers. The original size of WXY is 82°. what is the size of the angle after the sequence of rotations?

Given:

It underwent a sequence of two rotations around different centers.

To find:

The size of the angle WXY after the sequence of rotations.

Solution:

We know that, rotation is a rigid transformation. It means, the size and shape of the figure remains the same after the rotations. It other words, the figure and its image are congruent after rotation.

So, the measure of angle WXY remains same after the sequence of rotations, i.e.,

where, is the image of  after the sequence of rotations.

Therefore, the size of the angle WXY after the sequence of rotations is 82°.