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In the image, triangle \( ABC \) is dilated with a scale factor of \( \frac{1}{3} \), and we are tasked with labeling the angle measurements in triangle \( A'B'C' \).

Since dilation preserves the angle measurements of a triangle, the angles in triangle \( A'B'C' \) will be identical to those in triangle \( ABC \). Here’s how to label the angles in \( A'B'C' \) based on the provided measurements in triangle \( ABC \):

1. \( \angle A' \) corresponds to \( \angle A = 21^\circ \).
2. \( \angle B' \) corresponds to \( \angle B = 51^\circ \).
3. \( \angle C' \) corresponds to \( \angle C = 108^\circ \).

Thus, the angle labels for triangle \( A'B'C' \) should be:

- \( \angle A' = 21^\circ \)
- \( \angle B' = 51^\circ \)
- \( \angle C' = 108^\circ \)

Would you like further details on the dilation process or more information on similar triangles?

Here are some additional questions you might find interesting:
1. What happens to the side lengths when a triangle is dilated with a scale factor of \( \frac{1}{3} \)?
2. How does a scale factor affect the perimeter of a dilated triangle?
3. Does dilation affect the area of a triangle? If so, by what factor?
4. What are the properties of similar triangles?
5. How would the angle measures change if the dilation was a reflection instead?

**Tip:** When working with dilations, remember that angle measures stay the same, but side lengths are scaled by the given factor.

Triangle ABC is dilated with a scale factor of 1/3. Label the angle measurements in triangle A'B'C'.

Learn how to label angle measurements in a triangle after dilation with a scale factor of 1/3. This problem explores concepts of dilation, angle preservation, and similarity in triangles. Suitable for students in Grades 8-10.

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