Solve for x in (5x + 5)° (6x + 10)° in Geometry Problem

It seems like you're dealing with an equation involving angles in geometry. From the way you've written it, I assume we are working with the following scenario:

- You have two expressions for angles: \( (5x + 5)^\circ \) and \( (6x + 10)^\circ \).
- You likely need to determine their relationship. In geometry, these types of expressions often represent angles that could be supplementary, complementary, or form some other angle relationship.

Let's consider two cases:

### 1. **If the angles are supplementary:**
Supplementary angles sum to \( 180^\circ \). This gives us the equation:

\[
(5x + 5) + (6x + 10) = 180
\]

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

\[
5x + 5 + 6x + 10 = 180
\]

Combine like terms:

\[
11x + 15 = 180
\]

Subtract 15 from both sides:

\[
11x = 165
\]

Divide by 11:

\[
x = 15
\]

So, if the angles are supplementary, \( x = 15 \).

### 2. **If the angles are complementary:**
Complementary angles sum to \( 90^\circ \). This gives us the equation:

\[
(5x + 5) + (6x + 10) = 90
\]

Let's solve this case:

\[
5x + 5 + 6x + 10 = 90
\]

Combine like terms:

\[
11x + 15 = 90
\]

Subtract 15 from both sides:

\[
11x = 75
\]

Divide by 11:

\[
x = \frac{75}{11} \approx 6.82
\]

So, if the angles are complementary, \( x \approx 6.82 \).

### Conclusion:
- If the angles are supplementary, \( x = 15 \).
- If the angles are complementary, \( x \approx 6.82 \).

Would you like more details on either case, or clarification on how these relationships work in geometry?

### Related Questions:
1. How do you identify whether angles are complementary or supplementary?
2. What other types of angle relationships exist in geometry?
3. What are some real-world examples where supplementary angles are used?
4. Can angles be both complementary and supplementary at the same time?
5. How do we solve angle equations involving unknowns on both sides?

### Tip:
Always verify the type of angle relationship (complementary, supplementary, etc.) when solving for unknown angles in geometry.

Learn how to solve for x when dealing with angle relationships involving the expressions (5x + 5)° and (6x + 10)°. Explore how these angles can be supplementary or complementary and follow a step-by-step solution for both cases. Suitable for students in Grades 8-10.

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