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?

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.