https://file.aiquickdraw.com/mathbot/file/17316006579310l3ci9tl.jpg

To solve for the angle \( x \) in this pentagon, we can use the fact that the sum of the interior angles of a polygon with \( n \) sides is given by:

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

Since this is a pentagon (\( n = 5 \)), we calculate the sum of its interior angles as:

\[
(5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
\]

Now, we add up the known angles and set up an equation to solve for \( x \).

The known angles are:
- \( 57^\circ \)
- \( 27^\circ \)
- \( 131^\circ \)
- \( 61^\circ \)

Adding these:

\[
57^\circ + 27^\circ + 131^\circ + 61^\circ = 276^\circ
\]

Since the sum of all interior angles is \( 540^\circ \), we can find \( x \) by subtracting the sum of the known angles from \( 540^\circ \):

\[
x = 540^\circ - 276^\circ = 264^\circ
\]

Therefore, the value of \( x \) is \( 264^\circ \).

If you have further questions or need clarification, feel free to ask!

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### Related Questions to Explore Further:
1. How do you find the sum of interior angles for any polygon?
2. Why does a pentagon have a total of \( 540^\circ \) in its interior angles?
3. What would be the sum of the exterior angles of any polygon, and why?
4. How can you verify the calculation for the angle \( x \) using exterior angles?
5. How would the approach change if it were a regular pentagon (all angles and sides equal)?

### Tip:
For any polygon, the sum of the exterior angles is always \( 360^\circ \), regardless of the number of sides. This is a useful property when solving problems involving polygons.

Calculate the size of the angle marked x in the pentagon shown below.

Learn how to calculate a missing interior angle in a pentagon when four of the angles are known. This problem demonstrates the use of the polygon interior angle sum formula, making it suitable for students in Grades 8-10.

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