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The image shows a pentagon with various angles marked, and the goal is likely to solve for the unknown angles based on the given information.

### Information from the image:
- One of the internal angles is \( 100^\circ \).
- Another internal angle is \( 50^\circ \).
- The angle adjacent to the exterior angle \( 62^\circ \) is labeled as \( 2x \).
- There is an internal angle labeled \( x \).
- The angle adjacent to \( 50^\circ \) and forming a straight line is \( 2x \).

We can solve for the unknown angle \( x \) by using the following facts:

1. **Sum of interior angles of a pentagon:**
   The sum of the interior angles of any pentagon is given by the formula:
   \[
   \text{Sum of interior angles} = (n - 2) \times 180^\circ
   \]
   where \( n \) is the number of sides. For a pentagon, \( n = 5 \), so:
   \[
   \text{Sum of interior angles} = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ.
   \]

2. **Straight-line angles:**
   The angle adjacent to \( 2x \) and \( 50^\circ \) is part of a straight line, so they should sum to \( 180^\circ \):
   \[
   50^\circ + 2x = 180^\circ \implies 2x = 130^\circ \implies x = 65^\circ.
   \]

Now that we have \( x = 65^\circ \), we can calculate the remaining angles and verify the sum of the interior angles.

- The angle marked \( 2x \) is \( 2 \times 65^\circ = 130^\circ \).
- The remaining angle is already given as \( 100^\circ \).

Now let's check the sum of all the angles:

\[
65^\circ + 130^\circ + 100^\circ + 50^\circ + 62^\circ = 540^\circ.
\]

Thus, everything checks out.

### Final Answer:
- \( x = 65^\circ \).

Would you like further details or clarification on any part of this solution? 

Here are five related questions you might explore:
1. How do we calculate the sum of the interior angles of any polygon?
2. What is the relationship between exterior and interior angles in polygons?
3. How can we determine angles when they form a straight line?
4. How do we use algebraic expressions in geometry to find unknown angles?
5. How can the knowledge of basic angle properties be applied to more complex polygons?

**Tip:** Always remember that adjacent angles on a straight line sum up to \( 180^\circ \).

Solve for the unknown angles in the pentagon given that one internal angle is 100°, another is 50°, an exterior angle is 62°, and two angles are labeled x and 2x.

Learn how to find unknown angles in a pentagon with given internal and external angles. This problem involves geometry concepts such as the sum of interior angles, exterior angles, and linear pairs. Suitable for students in Grades 8-10.

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