The problem provides the following information:

• The measure of $\angle 1$ is 55°.
• Line $y$ is rotated 5° clockwise about the point of intersection.
• We are asked to find the new measure of $\angle 3$.

From the diagram, angles 1 and 3 appear to be vertical angles. Since vertical angles are congruent, the original measure of $\angle 3$ would also be 55°. However, when line $y$ is rotated 5° clockwise, $\angle 3$ will increase by 5° (because it is on the opposite side of the rotation).

Thus, the new measure of $\angle 3$ will be: $55^\circ + 5^\circ = 60^\circ$

The correct answer is 60°.

Let me know if you'd like further explanation or have more questions!

Here are 5 related questions for you:

1. What are vertical angles, and why are they always congruent?
2. How do rotations affect the angles formed by intersecting lines?
3. What are some properties of supplementary and complementary angles?
4. Can you describe how to rotate a line about a point in geometry?
5. What is the effect of counterclockwise rotations on angles in such diagrams?

Tip: Always check if the angle pairs are vertical, complementary, or supplementary when dealing with intersecting lines.