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To determine why the two triangles are similar, we can use the **Angle-Angle (AA) Similarity Postulate**. This postulate states that two triangles are similar if two pairs of corresponding angles are congruent (have the same measure).

Here’s the solution:

1. We are given that the measures of two pairs of corresponding angles are \( 24^\circ \) and \( 55^\circ \).
2. The sum of angles in any triangle is \( 180^\circ \).
3. For each triangle, the third angle can be calculated as:
   \[
   180^\circ - (24^\circ + 55^\circ) = 180^\circ - 79^\circ = 101^\circ
   \]
   This means the third angle in each triangle is \( 101^\circ \).
4. Now, we have three corresponding angles in the two triangles that are identical: \( 24^\circ \), \( 55^\circ \), and \( 101^\circ \).
5. Since the two triangles have two pairs of corresponding angles that are equal, by the **AA Similarity Postulate**, the triangles are similar.

### Final Answer:
The two triangles are similar because they have two pairs of corresponding angles that are congruent, satisfying the Angle-Angle (AA) Similarity Postulate.

Would you like more details on this solution, or have any questions?

Here are some related questions to expand your understanding:

1. How does the AA Similarity Postulate differ from other similarity criteria?
2. If only one angle pair was given, could the triangles still be similar?
3. What are other criteria for triangle similarity besides AA?
4. Can the AA postulate be applied to all polygons, or only triangles?
5. Why is the sum of angles in a triangle always \( 180^\circ \)?

**Tip:** When solving triangle similarity problems, always check for angle relationships or proportional sides.

The measures of two pairs of corresponding angles of two triangles are 24° and 55°. Explain why the two triangles are similar.

Understand why two triangles with corresponding angles of 24° and 55° are similar. This problem explores triangle similarity through the Angle-Angle (AA) Similarity Postulate, suitable for students in Grades 8-10.

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