https://file.aiquickdraw.com/mathbot/file/1726502351424q15zbujs.jpg

In the image provided, we have two adjacent angles on a straight line. The key idea is that the sum of these two angles should be equal to 180 degrees since they form a straight line (linear pair of angles).

We are given:

- One angle: \( 4n + 23 \)
- The other angle: \( n + 8 \)

Using the fact that the sum of the two angles equals 180 degrees:

\[
(4n + 23) + (n + 8) = 180
\]

Now, let's solve for \( n \):

1. Combine like terms:
   \[
   4n + n + 23 + 8 = 180
   \]
   \[
   5n + 31 = 180
   \]

2. Subtract 31 from both sides:
   \[
   5n = 180 - 31
   \]
   \[
   5n = 149
   \]

3. Divide both sides by 5:
   \[
   n = \frac{149}{5}
   \]
   \[
   n = 29.8
   \]

Thus, the value of \( n \) is approximately 29.8.

Would you like to go over any details or ask further questions?

Here are five related questions you can explore:
1. How do we know the sum of the angles is 180 degrees?
2. What other types of angle pairs could we encounter in geometry?
3. How would the problem change if the angles were complementary instead of supplementary?
4. Could the value of \( n \) be a whole number in a similar problem?
5. How would you check if the calculated value of \( n \) is correct?

**Tip**: When solving for a variable in geometry, always check the relationships between the angles—such as supplementary, complementary, or vertical—to ensure you're using the correct equation.

Solve for the missing variable given two angles on a straight line: (4n + 23) and (n + 8).

Learn how to solve for the variable n in a linear pair of angles, where (4n + 23) and (n + 8) form angles on a straight line. This solution demonstrates key algebraic techniques and the linear pair angle theorem. Suitable for students in Grades 8-10.

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