https://file.aiquickdraw.com/mathbot/file/1724764936872wrmz4eyx.jpg

To solve for \( x \) in the provided image, I need to analyze each shape and the angles marked within them. Since the image contains quadrilaterals, I will use the fact that the sum of the interior angles in any quadrilateral is \( 360^\circ \). Let's break down each shape:

1. **Top-left quadrilateral**:
    - The angles given are \( 72^\circ \), \( 118^\circ \), \( x \), and one unmarked angle.
    - The sum of the angles should be \( 360^\circ \).
    - Therefore, \( 72^\circ + 118^\circ + x + \text{unmarked angle} = 360^\circ \).

2. **Top-right quadrilateral**:
    - The angles given are \( x \), \( 107^\circ \), and \( 125^\circ \).
    - We can use a similar approach to find \( x \).

3. **Bottom-left quadrilateral**:
    - The angles given are \( 142^\circ \), \( x \), and \( 108^\circ \).
    - Again, the sum should be \( 360^\circ \).

I'll start by analyzing each one to solve for \( x \). Let me extract the information step by step from the image.The solutions for \( x \) in each quadrilateral depend on the unmarked fourth angle, denoted as \( \text{angle}_4 \):

1. **Top-left quadrilateral**: \( x = 170^\circ - \text{angle}_4 \)
2. **Top-right quadrilateral**: \( x = 128^\circ - \text{angle}_4 \)
3. **Bottom-left quadrilateral**: \( x = 110^\circ - \text{angle}_4 \)

To determine the exact value of \( x \), the fourth angle (which is not provided in the image) is necessary. However, these expressions provide the relationship between \( x \) and the unknown angle.

Would you like more details, or do you have any questions about the steps involved?

Here are 5 related questions that expand on the concepts:

1. How do you calculate the sum of interior angles for any polygon?
2. What are some properties of quadrilaterals that might help in solving these types of problems?
3. How would you solve for \( x \) if the fourth angle was given?
4. What are the specific properties of parallelograms regarding their angles?
5. How can you determine if a given quadrilateral is a specific type, like a trapezoid or a kite?

**Tip:** When solving for unknown angles in polygons, always ensure that you account for all angles and their relationships, especially when dealing with quadrilaterals or other polygons with complex angle arrangements.

Learn how to solve for x in quadrilaterals using geometry principles. This problem involves finding unknown angles in quadrilaterals by applying the sum of interior angles theorem. Detailed step-by-step explanations and related questions provided.

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