https://r2.erweima.ai/mathbot/image/1725582374980xqrubqhm.jpg

From the image, the problem involves two right-angled triangles \(ABC\) and \(ADE\) with the following information provided:

- \( \angle DAE = 25^\circ \)
- \( AC = DE \)
- \( AE = BC \)

The problem asks to determine an unknown angle, and there are four multiple-choice options: \(60^\circ\), \(80^\circ\), \(90^\circ\), and \(180^\circ\).

### Interpretation and Solution:
Given that triangles \(ABC\) and \(ADE\) are right-angled, let's analyze the angles and relationships between them.

- In triangle \(ADE\), we know \( \angle DAE = 25^\circ \) and it is a right triangle, so \( \angle ADE = 90^\circ \). Therefore, the remaining angle \( \angle AED \) can be found as:

\[
 \angle AED = 180^\circ - ( \angle DAE + \angle ADE ) = 180^\circ - (25^\circ + 90^\circ) = 65^\circ
\]

- Since the triangles are similar, the angle structure of triangle \(ABC\) will follow the same pattern due to the congruent side lengths. Therefore, the unknown angle requested, which is likely \( \angle ACB \), is \( 90^\circ \) (since \(ABC\) is also a right-angled triangle).

Thus, the correct answer to the problem should be **C) 90°**.

Would you like more details or have any questions? Here are 5 related questions to deepen understanding:

1. How do we determine angle congruence in similar triangles?
2. What are the properties of right-angled triangles that simplify angle calculations?
3. How can side ratios be used to confirm similarity between triangles?
4. Why is angle \( \angle AED \) equal to 65° in this problem?
5. How do known angles in one triangle help solve for unknown angles in another?

**Tip:** In geometry, triangles with equal angles are similar, meaning their sides are proportional, which can be used to solve many problems involving unknown lengths or angles.

In the given diagram, triangles ABC and ADE are right-angled with the following information: AC = DE, AE = BC, and angle DAE = 25°. Determine the unknown angle.

Solve the geometry problem involving right-angled triangles ABC and ADE with given conditions: AC = DE, AE = BC, and angle DAE = 25°. Learn how to determine the unknown angle using triangle similarity and angle sum properties. Suitable for students in Grades 8-10.

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