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The problem you've provided involves angles in a geometric figure. Here's how to approach it:

1. **Identify Given Information:**
   - \( \angle ABD = 65^\circ \)
   - The diagram shows a right angle at \( B \), meaning \( \angle ABC = 90^\circ \).

2. **Determine \( \angle DBC \):**
   - Since \( \angle ABC \) is a right angle and \( \angle ABD \) is given as \( 65^\circ \), we can find \( \angle DBC \) by using the fact that the sum of angles in a straight line is \( 180^\circ \).
   - Therefore, \( \angle DBC = \angle ABC - \angle ABD = 90^\circ - 65^\circ = 25^\circ \).

So, \( \angle DBC \) is **25 degrees**.

Would you like more details on how the angles were calculated, or do you have any other questions?

Here are some related questions to consider:

1. How would you find the value of \( \angle ABC \) if \( \angle DBC \) was known?
2. Can you determine the value of \( \angle ABD \) if \( \angle DBC \) was \( 30^\circ \)?
3. How can you verify that \( \angle ABC \) is indeed \( 90^\circ \) from the diagram?
4. What would be the effect on \( \angle DBC \) if \( \angle ABD \) were increased?
5. How can this problem help you understand the relationship between adjacent angles in geometry?

**Tip:** Always remember that the sum of angles around a point on a straight line is \( 180^\circ \), and this can be very useful in solving angle-related problems!

This guide explains how to find the angle ∠DBC when m∠ABD = 65° in a right triangle. Learn about the sum of angles in a triangle and apply the right angle theorem to solve this geometry problem, suitable for students in Grades 6-8.

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