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The problem states that the two triangles are congruent. Since the figures are congruent, corresponding angles and sides will be equal.

### Given Information:
- In triangle **BCD**:
  - \( \angle B = 75^\circ \)
  - \( \angle C = 45^\circ \)
  - \( \angle D = 60^\circ \)

- In triangle **IJK**:
  - \( \angle K = 60^\circ \)
  - \( \angle J = 45^\circ \)

### Find \( m \angle I \):
Since the two triangles are congruent, the corresponding angles must be equal. Therefore:
- \( \angle D \) corresponds to \( \angle K \), both of which are \( 60^\circ \).
- \( \angle C \) corresponds to \( \angle J \), both of which are \( 45^\circ \).
- \( \angle B \) corresponds to \( \angle I \).

Therefore:
\[
m \angle I = \angle B = 75^\circ
\]

Would you like more details or have other questions?

### Relative Questions:
1. What is the definition of congruent triangles?
2. How do we identify corresponding parts in congruent triangles?
3. Can two triangles with equal angles but different side lengths be congruent?
4. What other conditions besides congruency lead to equality of angles between two triangles?
5. How does the angle sum property of a triangle relate to this problem?

### Tip:
Always double-check for corresponding parts in congruent triangles to accurately identify equal measures.

These figures are congruent. What is m∠I?

Solve for the missing angle m∠I in congruent triangles using the property of corresponding angles. This problem covers key concepts such as congruent triangles and the angle sum property. Suitable for students in Grades 7-9.

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