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This problem involves the quadrilateral \( ABCD \), where \( AB = BC = AD \) and \( \angle DAB = 90^\circ \). The given angles in the figure are \( \angle ABC = 60^\circ \) and \( \angle CDA = x \). We are asked to find the value of \( x \).

### Step-by-step Solution:

1. **Identify the shape:**
   Since \( AB = BC = AD \) and \( \angle DAB = 90^\circ \), the quadrilateral \( ABCD \) forms an isosceles triangle for \( \triangle ABC \) and a quadrilateral with specific angle conditions.

2. **Sum of angles in a triangle:**
   In \( \triangle ABC \), the sum of the angles must equal \( 180^\circ \).
   \[
   \angle ABC + \angle ACB + \angle BAC = 180^\circ
   \]
   We know \( \angle ABC = 60^\circ \) and \( \angle BAC = 90^\circ \), so:
   \[
   60^\circ + \angle ACB + 90^\circ = 180^\circ
   \]
   Simplifying this:
   \[
   \angle ACB = 30^\circ
   \]

3. **Using angle sum in quadrilateral:**
   The sum of all internal angles of any quadrilateral is \( 360^\circ \).
   \[
   \angle DAB + \angle ABC + \angle BCD + \angle CDA = 360^\circ
   \]
   Substituting the known values:
   \[
   90^\circ + 60^\circ + 30^\circ + x = 360^\circ
   \]
   Simplifying:
   \[
   180^\circ + x = 360^\circ
   \]
   \[
   x = 180^\circ
   \]

4. **Final value of \( x \):**
   The value of \( x = 180^\circ \), but this seems incorrect based on the choices provided. Let's analyze the options.

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Let me check the options again and re-evaluate the calculation.

ABCD চতুর্ভুজীর AB = BC = AD এবং ∠DAB = 90° হলে x এর মান হবে

Learn how to find the value of angle x in a quadrilateral ABCD where AB = BC = AD and ∠DAB = 90°. This problem involves using geometry concepts such as the angle sum property and properties of isosceles triangles. Suitable for students in Grades 8-10.

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