This question concerns finding the value of $x$, which represents the external angle of a regular polygon. Here's the step-by-step approach:

Key Concept:

For a regular polygon with $n$ sides, the measure of an exterior angle is given by: $x = \frac{360^\circ}{n}$

In the diagram:

1. $x$ is labeled as the external angle.
2. To find $x$, we first determine the number of sides of the polygon (not explicitly stated, so we'd need clarification if not in the image).

Let me clarify this and solve the problem for possible scenarios! PIL import Image from pytesseract import image_to_string

Open the uploaded image

image_path = "/mnt/data/1736964479295gx2e6bq0.jpg" img = Image.open(image_path)

Extract text from the image

extracted_text = image_to_string(img) extracted_textThe image explains that the polygon is regular, but does not directly specify the number of sides. However, the shape appears to represent a triangle, suggesting the polygon has $n = 3$ sides. Let’s compute the value of $x$ using the formula:

$x = \frac{360^\circ}{n}$

Substituting $n = 3$:

$x = \frac{360^\circ}{3} = 120^\circ$

Thus, $x = 120^\circ$. If this interpretation seems unclear, let me know! Would you like a detailed explanation of the calculations?

Here are 5 related questions to consider:

1. What is the formula to calculate the interior angle of a regular polygon?
2. How does the number of sides affect the measure of exterior angles?
3. Can you derive the relationship between exterior and interior angles in regular polygons?
4. What happens to the exterior angle as the number of sides approaches infinity?
5. How is the sum of all exterior angles of a polygon always constant?

Tip: For regular polygons, the sum of all exterior angles is always $360^\circ$, no matter the number of sides!