The image contains a geometric problem. Let's break it down.

We are given a triangle $\triangle ABC$ with:

• $\angle BDC = 96^\circ$
• $\angle BAD = 30^\circ$
• $\angle DAB = \text{same as } \angle BAD = 30^\circ$

The task is to find $\angle ABD$.

Approach:

We can use the fact that the sum of angles in a triangle is always $180^\circ$.

To clarify the notation:

• In $\triangle ABD$, the sum of angles is: $\angle BAD + \angle ABD + \angle BDA = 180^\circ$
• Since $\angle BAD = 30^\circ$, we now need to find $\angle BDA$ from the available information to solve for $\angle ABD$.

Let me compute the value for $\angle ABD$.The value of $\angle ABD$ is $66^\circ$.

Would you like further details or have any questions? Here are 5 related questions to explore further:

1. How do you calculate the sum of angles in a triangle?
2. What is the concept of supplementary angles in geometry?
3. Can you explain how to apply the angle sum property to other polygons?
4. How would the problem change if one of the given angles was obtuse?
5. What role does the $96^\circ$ angle play in the configuration of this problem?

Tip: Remember, in any triangle, the sum of the interior angles always equals $180^\circ$, which is crucial for solving problems involving unknown angles.