1. **Stating the problem:** We need to find the value of the angle $\angle BAD$ in the given square $ABCD$. 2. **Understanding the figure:** The figure is a square with vertices $A$, $B$, $C$, and $D$. By definition, all sides of a square are equal in length, and all interior angles are right angles ($90^\circ$). 3. **Properties of a square:** - All sides are equal: $AB = BC = CD = DA$. - All interior angles are $90^\circ$. - The angle at each vertex is a right angle. 4. **Identifying $\angle BAD$:** The angle $\angle BAD$ is the angle formed at vertex $A$ by points $B$ and $D$. 5. **Since $ABCD$ is a square, the angle at vertex $A$ is $90^\circ$.** 6. **Therefore, the value of $\angle BAD$ is:** $$\angle BAD = 90^\circ$$ **Final answer:** $\boxed{90^\circ}$