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The problem given is in Malay, and the key elements in the question can be translated as follows:

**Translation of the text:**
- The diagram shows part of polygons \( A \) and \( B \).
- \( A \) is a regular polygon with \( n \) sides.
- \( B \) is a regular hexagon.
- The internal angle between polygons \( A \) and \( B \) is \( 84^\circ \).
- Determine the value of \( n \).

### Approach:

1. **Regular Polygon Properties:**
   - The internal angle of a regular polygon with \( n \) sides can be calculated using the formula:
   \[
   \text{Internal angle of polygon A} = \frac{(n-2) \times 180^\circ}{n}
   \]
   - For a regular hexagon \( B \) (which has 6 sides), the internal angle is:
   \[
   \text{Internal angle of polygon B} = \frac{(6-2) \times 180^\circ}{6} = 120^\circ
   \]
   
2. **External Angles:**
   - The external angle is the supplement of the internal angle. For polygon \( A \):
   \[
   \text{External angle of A} = 180^\circ - \frac{(n-2) \times 180^\circ}{n} = \frac{360^\circ}{n}
   \]
   - For polygon \( B \), the external angle is:
   \[
   \text{External angle of B} = 180^\circ - 120^\circ = 60^\circ
   \]

3. **Given Relationship:**
   - The sum of the external angles at the vertex where polygons \( A \) and \( B \) meet is \( 84^\circ \), so:
   \[
   \frac{360^\circ}{n} + 60^\circ = 84^\circ
   \]

4. **Solve for \( n \):**
   \[
   \frac{360^\circ}{n} = 24^\circ
   \]
   \[
   n = \frac{360^\circ}{24^\circ} = 15
   \]

Thus, the value of \( n \) is **15**.

Would you like any additional details, or do you have any further questions?

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Here are 5 related questions for further exploration:
1. How can we derive the internal angle formula for any regular polygon?
2. What is the relationship between internal and external angles of polygons?
3. Can you find the sum of the internal angles for any polygon with \( n \) sides?
4. How does the concept of tessellation relate to regular polygons?
5. What is the significance of the external angle sum in any polygon?

**Tip:** For any regular polygon, the internal angle increases as the number of sides increases.

Diagram above shows parts of polygons A and B. A is a regular polygon with n sides. B is a regular hexagon. The internal angle between polygons A and B is 84°. Determine the value of n.

Learn how to find the number of sides of a regular polygon based on its angle with a regular hexagon. This problem explores the relationship between internal and external angles and applies the polygon angle-sum theorem. Suitable for Grades 9-11 students.

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