https://file.aiquickdraw.com/mathbot/file/17263865139791qpczx33.jpg

To solve for \( x \) in this image, we can use the fact that the shape in the image is a polygon, and the sum of the interior angles of any polygon can be calculated by the formula:

\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\]

Where \( n \) is the number of sides. This polygon has 5 sides, so we can calculate the sum of the interior angles:

\[
\text{Sum of angles} = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
\]

We are given the angles \( 140^\circ \), \( 150^\circ \), and \( 130^\circ \), and we need to find \( x \). The sum of all the angles should equal 540°, so we can set up the following equation:

\[
140^\circ + 150^\circ + 130^\circ + x = 540^\circ
\]

Now, let's solve for \( x \):

\[
420^\circ + x = 540^\circ
\]

\[
x = 540^\circ - 420^\circ = 120^\circ
\]

So, the value of \( x \) is \( 120^\circ \).

Do you have any questions or would you like a more detailed explanation?

Here are 5 related questions to further expand your understanding:
1. How do we find the sum of the interior angles of any polygon?
2. What is the formula to calculate the sum of exterior angles of a polygon?
3. How does the shape of a polygon affect its interior angles?
4. What are the properties of regular polygons regarding angles?
5. What would be the sum of interior angles for a hexagon?

**Tip:** When solving problems involving polygons, always check how many sides the polygon has, as this will help determine the sum of its interior angles.

Find the value of y (x) in a polygon with given angles of 140°, 150°, 130°, and unknown angle x.

Learn how to find the missing angle in a pentagon with given angles of 140°, 150°, and 130°. Use the sum of interior angles formula to solve this step-by-step geometry problem, ideal for Grades 8-10.

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