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The problem asks to find the angles \(a\), \(b\), \(c\), and \(d\) where two straight lines intersect at a point. The equation given is \(b + c + d = 280^\circ\).

### Step 1: Use angle relationships at the intersection
Since two straight lines intersect, the sum of angles around the point must equal \(360^\circ\).

Thus, the sum of all four angles is:
\[
a + b + c + d = 360^\circ
\]

### Step 2: Substitute the given equation
We know that \(b + c + d = 280^\circ\). Substituting this into the total sum equation:
\[
a + 280^\circ = 360^\circ
\]

### Step 3: Solve for \(a\)
\[
a = 360^\circ - 280^\circ = 80^\circ
\]

### Step 4: Use vertical angle property
From the diagram, angle \(a\) is vertically opposite to angle \(c\), so:
\[
a = c
\]
Thus, \(c = 80^\circ\).

### Step 5: Solve for \(b\) and \(d\)
Now, using \(b + c + d = 280^\circ\) and \(c = 80^\circ\), substitute \(c\) into the equation:
\[
b + 80^\circ + d = 280^\circ
\]
\[
b + d = 200^\circ
\]

Finally, notice that \(b\) and \(d\) are vertically opposite, so:
\[
b = d
\]
Thus:
\[
2b = 200^\circ
\]
\[
b = 100^\circ
\]
Since \(b = d\), \(d = 100^\circ\).

### Conclusion:
The angles are:
- \(a = 80^\circ\)
- \(b = 100^\circ\)
- \(c = 80^\circ\)
- \(d = 100^\circ\)

Would you like further details or have any questions?

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Here are five related questions to deepen understanding:
1. What is the sum of the angles at a point where two lines intersect?
2. How do vertical angles relate to each other?
3. How would you solve if the given equation was \(a + b + d = 300^\circ\)?
4. How can supplementary angles be used to solve intersection problems?
5. What would change if the two lines were not straight but curved?

**Tip:** Vertical angles are always equal when two lines intersect, which simplifies finding unknown angles.

Two straight lines cross at a point. Given that b + c + d = 280°, work out the sizes of angles a, b, c, and d.

Solve the problem of finding angles formed at the intersection of two straight lines where b + c + d = 280°. This detailed explanation covers the sum of angles at a point and the concept of vertical angles. Suitable for students in Grades 7-9.

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