https://r2.erweima.ai/mathbot/image/1726510154728ezamnexr.jpg

To solve for \( x \) in this problem, we need to use the fact that the angles shown in the image are **vertically opposite angles**, which are always equal.

We are given two expressions for the angles:
1. \( 8x + 36^\circ \)
2. \( 5x + 60^\circ \)

Since these are vertically opposite angles, we can set the expressions equal to each other:
\[
8x + 36^\circ = 5x + 60^\circ
\]

### Step-by-step solution:
1. **Subtract \( 5x \) from both sides** to get the terms with \( x \) on one side:
   \[
   8x - 5x + 36^\circ = 60^\circ
   \]
   Simplifying:
   \[
   3x + 36^\circ = 60^\circ
   \]

2. **Subtract 36° from both sides** to isolate the \( x \)-term:
   \[
   3x = 60^\circ - 36^\circ
   \]
   Simplifying:
   \[
   3x = 24^\circ
   \]

3. **Divide both sides by 3** to solve for \( x \):
   \[
   x = \frac{24^\circ}{3} = 8^\circ
   \]

Thus, the value of \( x \) is \( 8^\circ \).

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

### Related questions:
1. What are vertically opposite angles, and why are they equal?
2. Can this type of equation arise in other geometric problems?
3. How would you solve the equation if more terms were involved on both sides?
4. What happens if the angles are supplementary instead of equal?
5. How can algebraic techniques help solve geometric angle problems like this?

**Tip:** When working with geometric equations, identifying relationships like complementary, supplementary, or vertically opposite angles helps set up the correct equations.

Encuentra el valor de x: 8x + 36° = 5x + 60°

Learn how to solve the vertically opposite angles equation 8x + 36° = 5x + 60° using basic algebra. This step-by-step solution is perfect for students in Grades 6-8, covering key concepts like vertically opposite angles and algebraic manipulation.

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