https://file.aiquickdraw.com/mathbot/file/1726768184827c6kokyb9.jpg

To solve for \( n \) in the given diagram, we first need to apply the properties of angles. In the image, two key observations can be made:

1. There is a right angle (90°) formed between the two intersecting lines, which creates two supplementary angles.
2. The angles given are \( (2n + 7)^\circ \) and \( (3n + 3)^\circ \).

Since these two angles form a right angle (90°), we can write the equation:

\[
(2n + 7) + (3n + 3) = 90
\]

Now, let's solve this equation:

\[
2n + 7 + 3n + 3 = 90
\]

Combine like terms:

\[
5n + 10 = 90
\]

Subtract 10 from both sides:

\[
5n = 80
\]

Finally, divide both sides by 5:

\[
n = 16
\]

Thus, the value of \( n \) is 16.

Would you like more details, or do you have any questions about this solution?

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Here are 5 related questions for further practice:
1. What is the measure of each angle when \( n = 16 \)?
2. What are supplementary and complementary angles?
3. If one of the angles were \( (4n - 2)^\circ \), how would you adjust the equation?
4. How do you identify vertical angles, and what properties do they have?
5. What is the difference between alternate interior angles and corresponding angles in geometry?

**Tip:** When solving for unknowns in geometry problems involving angles, always check if the angles form supplementary, complementary, or right angles to guide your equation setup.

Solve for the value of n. Given angles are (2n + 7)° and (3n + 3)° forming a right angle.

Learn how to solve for the value of n in a geometry problem involving angles. The two given angles (2n + 7)° and (3n + 3)° form a right angle. This step-by-step guide explains the algebraic setup and solution, suitable for students in Grades 7-10.

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