https://file.aiquickdraw.com/mathbot/file/1724576818590lvyi25qv.jpg

Let's analyze the new image to find the value of \( x \).

### Description and Analysis:

The image depicts a quadrilateral with the following angles labeled:
- One angle is \( x^\circ \) (the value we need to find).
- Another angle is \( 50^\circ \).
- There is a right angle (\( 90^\circ \)).
- The fourth angle is \( 120^\circ \).

### Solution:

The sum of the interior angles of any quadrilateral is always \( 360^\circ \). We can set up the equation for the sum of the angles in this quadrilateral.

1. Sum of the angles:
   \[
   x^\circ + 50^\circ + 90^\circ + 120^\circ = 360^\circ
   \]
2. Combine the known angles:
   \[
   x^\circ + 260^\circ = 360^\circ
   \]
3. Solving for \( x \):
   \[
   x^\circ = 360^\circ - 260^\circ = 100^\circ
   \]

Thus, the value of \( x \) is \( 100^\circ \).

Would you like more details or have any additional questions?

### Follow-up Questions:
1. How would the calculation change if this were a pentagon instead of a quadrilateral?
2. Why is the sum of the interior angles of a quadrilateral always \( 360^\circ \)?
3. Can the sum of the angles in a quadrilateral ever be different from \( 360^\circ \)?
4. How would you verify your answer using a protractor?
5. What are the properties of special types of quadrilaterals like rectangles and squares regarding their angles?

### Tip:
When solving for unknown angles in polygons, always start by recalling the sum of the interior angles for that shape. For a quadrilateral, it's \( 360^\circ \), which is fundamental to solving for unknown angles.

Learn how to find the value of x in a quadrilateral using the sum of interior angles theorem. This problem involves identifying angles in a quadrilateral and applying the concept of angle sum. Suitable for Grades 7-9 students studying geometry.

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