https://file.aiquickdraw.com/mathbot/file/1728430202815trnm34p4.jpg

The problem involves two similar quadrilaterals \( P'Q'R'S' \) and \( PQRS \). We're given that:

- \( P', Q', R', S' \) correspond to \( P, Q, R, S \), respectively.
- The measure of angle \( P \) is 30°, angle \( Q \) is 50°, and angle \( R \) is 70°.
- The side lengths of quadrilateral \( P'Q'R'S' \) are three times the corresponding side lengths of \( PQRS \).
- We are asked to find the measure of angle \( P' \).

Since the two quadrilaterals are similar, the corresponding angles of similar figures are congruent. This means:

\[
\angle P' = \angle P = 30^\circ
\]

The size of the side lengths does not affect the angles in similar shapes, as similarity preserves angle measures.

Thus, the correct answer is:
\[
\boxed{30^\circ}
\]

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

### Related Questions:
1. What are the properties of similar quadrilaterals?
2. How do side ratios affect the properties of similar figures?
3. Can angles change in similar shapes with different size scaling?
4. What happens to the area when side lengths of a similar figure are scaled by a factor of 3?
5. How are the diagonals of similar quadrilaterals related?

### Tip:
In similar figures, even if side lengths change by a ratio, the corresponding angles remain the same!

Quadrilateral P'Q'R'S' is similar to quadrilateral PQRS, where P, Q, R, and S correspond to P', Q', R', and S', respectively. The measure of angle P is 30°, the measure of angle Q is 50°, and the measure of angle R is 70°. The length of each side of P'Q'R'S' is 3 times the length of each corresponding side of PQRS. What is the measure of angle P'?

Learn how to determine the measure of an angle in a similar quadrilateral when given corresponding angles and side length ratios. This problem explores the properties of similar figures and angle congruence, suitable for Grades 8-10.

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