https://file.aiquickdraw.com/mathbot/file/1726752882278kajn7se3.jpg

In the image, we are given two angles: \((5p + 7)^\circ\) and \((3p - 5)^\circ\), which together form a right angle. Since the sum of angles forming a right angle is \(90^\circ\), we can set up the equation:

\[
(5p + 7) + (3p - 5) = 90
\]

Now, let's solve for \(p\).

1. Combine like terms:
\[
5p + 3p + 7 - 5 = 90
\]
\[
8p + 2 = 90
\]

2. Subtract 2 from both sides:
\[
8p = 88
\]

3. Divide by 8:
\[
p = \frac{88}{8} = 11
\]

So, the value of \(p\) is \(11\).

Would you like a more detailed explanation or have any questions?

Here are five related questions to deepen understanding:
1. How would you solve this problem if the sum of angles formed a different type of angle (e.g., straight angle)?
2. What are complementary angles, and how do they relate to this problem?
3. If one angle was doubled, how would that affect the equation?
4. How can you check the solution to ensure it is correct?
5. Can you generalize this approach for angles involving more complex expressions?

**Tip:** Always verify the sum of angles in geometry problems to avoid calculation mistakes!

Solve for the value of p given the equation formed by the angles (5p + 7)° and (3p - 5)° that together form a right angle.

Learn how to solve for p in the equation (5p + 7) + (3p - 5) = 90, which involves using algebra and understanding angles that form a right angle. This problem is suitable for students in Grades 7-9.

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