To solve the problem depicted in the image:

We are asked to find $\angle CAO$ in the given diagram. Here's the information provided:

• $ABCD$ is a square.
• $ADEO$ is a rectangle.
• Diagonals $AC$ and $DF$ intersect at point $O$.
• $\angle COD = 72^\circ$.

Step-by-Step Solution:

1. Properties of the square $ABCD$:

   • The diagonals of a square bisect each other at $90^\circ$.
   • Therefore, $\angle AOD = 90^\circ$.

2. Using angle sum property at $O$: In $\triangle COD$, the sum of angles at $O$ is: $\angle AOD + \angle COD + \angle CAO = 180^\circ$

3. Substitute known values: $90^\circ + 72^\circ + \angle CAO = 180^\circ$

4. Solve for $\angle CAO$: $\angle CAO = 180^\circ - 90^\circ - 72^\circ = 18^\circ$

Final Answer:

$\boxed{18^\circ}$

Would you like a detailed explanation of the properties of the diagonals in squares or rectangles?

Here are 5 questions that expand on this topic:

1. What are the properties of diagonals in a square, and how do they help in angle calculations?
2. How can the angle sum property of a triangle be applied in problems involving intersecting diagonals?
3. What is the significance of the rectangle $ADEO$ in this problem?
4. How can symmetry in geometrical shapes simplify problem-solving?
5. What other methods can verify the result of $\angle CAO = 18^\circ$?

Tip:

When working with geometry problems involving squares or rectangles, always check for symmetry and properties of diagonals—they often simplify calculations!