https://file.aiquickdraw.com/mathbot/file/1726768289614bqd5zzij.jpg

In this problem, the figure shows a straight angle, meaning the sum of the angles must equal 180°. The given angles are:

- \( 37^\circ \)
- \( (7n - 3)^\circ \)
- A right angle, which is \( 90^\circ \).

We can set up an equation based on the sum of these angles:

\[
37^\circ + (7n - 3)^\circ + 90^\circ = 180^\circ
\]

Let's solve this step-by-step.

1. Combine the constants on the left-hand side:
\[
37 + (7n - 3) + 90 = 180
\]
\[
(37 - 3 + 90) + 7n = 180
\]
\[
124 + 7n = 180
\]

2. Subtract 124 from both sides:
\[
7n = 180 - 124
\]
\[
7n = 56
\]

3. Finally, divide by 7 to solve for \( n \):
\[
n = \frac{56}{7} = 8
\]

Thus, the value of \( n \) is 8.

Would you like further details on this solution, or do you have any questions?

Here are 5 related questions to deepen your understanding:
1. What would happen if one of the angles was unknown? How would we solve for that?
2. How can we verify that the angles sum to 180° in this specific diagram?
3. What is the importance of the right angle in this problem?
4. How does the straight line in the figure help us set up the equation?
5. If the angle expression was different, say \( (7n + 3)^\circ \), how would that affect the solution?

**Tip:** Always check if the given angles form a special type of angle (like a straight angle or triangle), as this helps in setting up the correct equation.

Solve for the value of n in the given angle equation with angles 37°, (7n - 3)°, and a right angle (90°).

Learn how to solve for the variable n in an angle equation where the given angles are 37°, (7n - 3)°, and a right angle (90°). This problem involves key geometry concepts, such as the sum of angles in a straight line and linear equations. Suitable for Grades 7-9.

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