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In the provided image, you are asked to find the value of \( n \) for the angles in a triangle. The angles are given as follows:

1. \( (4n + 13)^\circ \)
2. \( (6n + 2)^\circ \)
3. \( (14n - 13)^\circ \)

Since the sum of the interior angles of any triangle is always \( 180^\circ \), we can set up the following equation:

\[
(4n + 13) + (6n + 2) + (14n - 13) = 180
\]

### Step-by-Step Solution:

1. Combine like terms:
   \[
   (4n + 6n + 14n) + (13 + 2 - 13) = 180
   \]
   \[
   24n + 2 = 180
   \]

2. Subtract 2 from both sides:
   \[
   24n = 178
   \]

3. Divide both sides by 24:
   \[
   n = \frac{178}{24} = 7.42
   \]

So, the value of \( n \) is approximately \( 7.42 \).

### Would you like more details or have any questions?

Here are 5 related questions:
1. What is the sum of the interior angles of a polygon with 6 sides?
2. How do we solve for unknowns when given more than three angles in a polygon?
3. What happens if one of the angles in a triangle is \(90^\circ\)? 
4. Can the angles in this triangle be checked for validity with the value of \(n\)?
5. How would this problem change if the triangle were scalene or isosceles?

**Tip:** When solving for unknowns in geometry, always check the sum of angles or properties of shapes to ensure your results are valid.

Find n for the triangle where the angles are: (4n + 13)°, (6n + 2)°, and (14n - 13)°.

Learn how to find the value of n in a triangle where the angles are given by (4n + 13)°, (6n + 2)°, and (14n - 13)°. This problem involves key concepts in algebra and geometry and is suitable for students in Grades 8-10.

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