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To calculate the size of angle \( x \), we can use the property that the sum of the exterior angles of any polygon is always \( 360^\circ \).

Here, we are given the exterior angles:
- \( 101^\circ \)
- \( 244^\circ \)
- \( 42^\circ \)
- \( 56^\circ \)
- \( x \) (unknown angle)

Now, apply the sum of the exterior angles:

\[
101^\circ + 244^\circ + 42^\circ + 56^\circ + x = 360^\circ
\]

Let's solve for \( x \).

\[
x = 360^\circ - (101^\circ + 244^\circ + 42^\circ + 56^\circ)
\]

\[
x = 360^\circ - 443^\circ
\]

\[
x = -83^\circ
\]

It seems there may be a misunderstanding because the exterior angle should not be negative. Could you clarify whether you were referring to the sum of the **interior** or **exterior** angles for this shape, or whether additional information is needed?

Would you like me to try a different method or review the problem?

---

In the meantime, here are five related questions:
1. How do you find the sum of interior angles in any polygon?
2. How is the sum of exterior angles always \( 360^\circ \) regardless of the number of sides?
3. Could an angle in a polygon ever be negative in standard geometric contexts?
4. What defines an exterior angle in a polygon compared to an interior angle?
5. How can we classify polygons based on their angle properties?

**Tip:** When working with polygons, ensure you know whether the problem involves **exterior** or **interior** angles, as they follow different summation rules.

Calculate the size of angle x. Given angles: 101°, 244°, 42°, and 56°.

Learn how to calculate the size of angle x in a polygon, using the exterior angle theorem. Given angles: 101°, 244°, 42°, and 56°. This step-by-step solution is suitable for Grades 7-10 geometry students.

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