Let's revisit the calculation with the information that \( x = 45^\circ \).

### Re-examining the Problem:

Given the equation for the sum of the interior angles in the quadrilateral:

\[
60^\circ + 2x^\circ + 75^\circ + x^\circ = 360^\circ
\]

We substitute \( x = 45^\circ \) into the equation:

\[
60^\circ + 2(45^\circ) + 75^\circ + 45^\circ = 360^\circ
\]

### Calculation:

1. Calculate \( 2(45^\circ) \):
   \[
   2 \times 45^\circ = 90^\circ
   \]

2. Add all the angles together:
   \[
   60^\circ + 90^\circ + 75^\circ + 45^\circ = 270^\circ
   \]

3. The sum is \( 270^\circ \), but it should be \( 360^\circ \).

### Conclusion:
If \( x = 45^\circ \), the total sum of the angles is only \( 270^\circ \), which doesn't satisfy the quadrilateral angle sum requirement of \( 360^\circ \).

Therefore, for the angles to add up to \( 360^\circ \), the value of \( x \) cannot be \( 45^\circ \). The correct value should be \( 75^\circ \), as calculated earlier.

Would you like to discuss this further or review any other part of the problem?

### Related Questions:

1. How do we solve for \( x \) if the quadrilateral were a trapezoid?
2. What is the significance of the angle sum property in polygons?
3. How would this approach differ for a cyclic quadrilateral?
4. Can the quadrilateral's sides influence the angle values?
5. How would you apply this method to find missing angles in a pentagon?

### Tip:

Always recheck calculations by substituting the found value back into the original equation to ensure it satisfies all the given conditions.

Explore how to solve for x in a quadrilateral using the angle sum property. Given angles 60°, 75°, and a double angle condition, find the correct value of x to ensure the total angle sum is 360°. Detailed step-by-step explanation and calculations provided.

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