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?

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.