We are given two straight lines intersecting at a point, forming four angles: $a$, $b$, $c$, and $d$. The problem states:

$b + c + d = 280^\circ$

Since the total angles around a point add up to $360^\circ$, we know that:

$a + b + c + d = 360^\circ$

Substituting $b + c + d = 280^\circ$ into this equation:

$a + 280^\circ = 360^\circ$

This simplifies to:

$a = 360^\circ - 280^\circ = 80^\circ$

Now that we know $a = 80^\circ$, we can use the relationship $a + b = 180^\circ$ because $a$ and $b$ are vertically opposite angles.

$80^\circ + b = 180^\circ$

This gives:

$b = 180^\circ - 80^\circ = 100^\circ$

Finally, since we know that $b + c + d = 280^\circ$ and $b = 100^\circ$, we can substitute this into the equation:

$100^\circ + c + d = 280^\circ$

Simplifying:

$c + d = 180^\circ$

Thus, $c$ and $d$ are also supplementary angles, but without more specific information about their individual values, we can conclude that:

$c + d = 180^\circ$

Let me know if you'd like further clarification on how $c$ and $d$ could be specified or if you have any other questions!

Here are 5 related questions:

1. What is the sum of all angles around a point?
2. How do vertically opposite angles relate to each other?
3. Can you always solve for individual angles without knowing more about supplementary pairs?
4. What are alternate interior angles, and how do they compare with vertically opposite angles?
5. How do straight line angles (linear pairs) relate to each other?

Tip: In problems involving intersecting lines, always start by identifying angles that are either supplementary or vertically opposite. This helps in simplifying the equation system.