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!