Question

In triangle PQR, the measure of angle Q is 37°. A rotation 53° counterclockwise about point Q is applied to triangle PQR to produce triangle STU. What is the measure of angle T?

Answer 1

37°

Explanation:

We need to use some facts about rotations and angles to answer your question. Here are some key points:

• A rotation is a transformation that turns a figure around a fixed point, called the center of rotation.
• The angle of rotation is the measure of how much the figure is rotated counterclockwise or clockwise.
• Rotations preserve the distance and orientation of the figure, which means that the length of the sides and the measure of the angles do not change.

Now, let’s apply these facts to your problem. You have a triangle PQR with angle Q = 37°, and you rotate it 53° counterclockwise about point Q to get triangle STU. Since Q is the center of rotation, it stays in the same place, so we can say that Q = T. Also, since rotations preserve angles, we can say that angle P = angle S and angle R = angle U. Therefore, angle T = angle Q = 37°.