The angles in each individual problem, based on the diagram provided, are being analyzed separately, not collectively as a set of angles. Here’s a breakdown of how each situation works:

1. **Problem 10**: 
   - You are given \( m\angle EBG = 60^\circ \). This angle is composed of two smaller angles: \( m\angle EBF \) and \( m\angle FBG \).
   - So here, we are only adding \( m\angle EBF \) and \( m\angle FBG \) to get \( m\angle EBG \). The sum \( x + 2x = 60^\circ \) applies only to the angles directly mentioned.

2. **Problem 11**:
   - \( m\angle ABE = 64^\circ \) and \( m\angle DBE = \) are supplementary angles because they lie on a straight line (ABE and DBE make a straight angle at point B).
   - Here, \( m\angle ABE + m\angle DBE = 180^\circ \) because the angles are on a straight line.

3. **Problem 12**:
   - \( m\angle GBH = 28^\circ \) and \( m\angle GBC \) are supplementary because they also lie on a straight line, and so \( m\angle GBH + m\angle GBC = 180^\circ \).

So, **for each pair of angles that lie on a straight line**, they do indeed add up to 180°. However, the angles in different problems are not related to each other and should not be added together across different problems.

Would you like to explore more details on this concept? Here are five related questions:

1. How do you determine when angles are on a straight line?
2. Can angles that are not adjacent still add up to 180°?
3. What are vertical angles, and do they also sum to 180°?
4. How does knowing one angle help find others in a multi-angle problem?
5. When dealing with multiple angles, how can you keep track of which angles add up to 180°?

**Tip:** In diagrams, always look for straight lines or intersecting lines to identify supplementary angles. This helps in quickly determining angle measures without much calculation.

Explore the angle sum property in geometry and understand when angles add up to 180 degrees. Detailed breakdowns of specific problems provided, including how to identify supplementary angles on straight lines.

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