https://r2.erweima.ai/mathbot/image/172303214804676ntsbzd.jpg

To find the value of \( x \) in the given geometric configuration, let's analyze the information provided in the image.

From the image, we can observe the following:
- There are two intersecting lines forming several angles.
- One of the angles is marked as \( (x - 28)^\circ \).
- Another angle adjacent to it is marked as \( 148^\circ \).

Since these two angles are on a straight line, they are supplementary angles, meaning their sum is \( 180^\circ \).

We can set up the following equation:

\[
(x - 28)^\circ + 148^\circ = 180^\circ
\]

Now, solve for \( x \):

\[
(x - 28) + 148 = 180
\]

Combine like terms:

\[
x + 120 = 180
\]

Subtract 120 from both sides:

\[
x = 60
\]

Therefore, the value of \( x \) is \( 60^\circ \).

Would you like more details or have any questions about this solution? Here are some additional questions to expand on this topic:

1. How do we determine supplementary angles in geometry?
2. What are complementary angles, and how are they different from supplementary angles?
3. How can we use algebra to solve for unknown angles in different geometric configurations?
4. Can you provide an example of vertically opposite angles and explain their properties?
5. What is the significance of alternate interior angles in parallel lines?
6. How do we calculate angles in a polygon, specifically a pentagon?
7. What is the relationship between angles and the properties of triangles?
8. How does the exterior angle theorem apply to triangles?

**Tip:** When working with angles, always remember to check for complementary, supplementary, and vertically opposite angles to simplify your calculations.

Learn how to find the value of x in a geometric configuration involving angles. Detailed step-by-step solution provided, covering supplementary angles and algebraic equations. Suitable for Grades 9-12 students studying geometry and algebra.

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