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The image presents a problem where we are asked to determine the relationships between angles labeled as \( a \), \( b \), \( c \), and \( d \), and whether these angles are supplementary, complementary, or vertical (opposite angles). Here’s how to approach this:

### 1. Identifying angle relationships:
- \( \angle a \) and \( \angle b \): These two angles are adjacent and form a straight line, so they are **supplementary**. The sum of supplementary angles is always \( 180^\circ \).
- \( \angle a \) and \( \angle d \): These are vertical (opposite) angles, so they are **equal**.
- \( \angle a \) and \( \angle c \): Like \( \angle a \) and \( \angle d \), \( \angle a \) and \( \angle c \) are also vertical angles, so they are **equal**.

### 2. Given angles:
- \( \angle b = 120^\circ \)
- \( \angle d = 120^\circ \)
- \( \angle a = 60^\circ \) (since it is supplementary to \( \angle b \))

### Completing the questions:
- \( a \) and \( d \) are **opposite angles**, so \( a = d = 60^\circ \).
- \( a \) and \( c \) are **opposite angles**, so \( a = c = 60^\circ \).

### Answering the questions in the activity:
1. **\( a \) y \( d \) = \( 60^\circ \)**
2. **\( a \) y \( c \) = \( 60^\circ \)**
3. **Los ángulos suplementarios suman = \( 180^\circ \)**
4. **Los ángulos complementarios suman = \( 90^\circ \)** (However, there are no complementary angles shown in this diagram.)

Would you like further details on these angle relationships, or do you have any other questions?

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Here are 5 related questions to explore:
1. What is the definition of vertical (opposite) angles?
2. How can you determine if two angles are supplementary or complementary?
3. What is the sum of all interior angles on a straight line?
4. Can two obtuse angles be supplementary? Why or why not?
5. What happens if two adjacent angles are both right angles?

**Tip:** Vertical (opposite) angles are always equal, no matter the orientation of the lines.

Determina si los ángulos son suplementarios, complementarios u opuestos por el vértice.

Learn how to determine whether angles are supplementary, complementary, or vertical using a geometric diagram. This problem covers angle relationships with real-world examples, suitable for students in Grades 6-8.

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