https://r2.erweima.ai/mathbot/image/1726351347666nvbg6yaa.jpg

To solve this problem, we need to find the sum of the angles \(a + b + c + d\).

From the image, we see that:

- The triangle's internal angle is \(67^\circ\) at the top.
- The angles \(a\), \(b\), \(c\), and \(d\) are exterior angles around the triangle.

### Key Concept:
- The sum of the exterior angles of any polygon is always \(360^\circ\).
- The triangle has three exterior angles formed at each vertex by extending the sides. 

### Step-by-step Solution:

1. The angles \(a\), \(b\), and \(d\) are exterior angles at each vertex of the triangle.
   - The exterior angle is supplementary to the interior angle, meaning \( \text{exterior angle} = 180^\circ - \text{interior angle}\).

2. The interior angles of a triangle add up to \(180^\circ\). In this case:
   - We already have one interior angle, which is \(67^\circ\). Let's call the other two angles \(x\) and \(y\).
   \[
   67^\circ + x + y = 180^\circ \quad \Rightarrow \quad x + y = 113^\circ
   \]

3. Each exterior angle is calculated as \(180^\circ - \text{interior angle}\):
   - For \(a\), the exterior angle corresponding to \(x\), we have:
     \[
     a = 180^\circ - x
     \]
   - For \(b\), the exterior angle corresponding to \(y\), we have:
     \[
     b = 180^\circ - y
     \]
   - For \(d\), the exterior angle corresponding to \(67^\circ\), we have:
     \[
     d = 180^\circ - 67^\circ = 113^\circ
     \]

4. The angle \(c\) is formed by extending the side of the triangle, making \(c\) an exterior angle on the other side. Using the rule that the exterior angles sum to \(360^\circ\), we can say:
   \[
   a + b + c + d = 360^\circ
   \]
   Now, adding the known values, we get the total:
   \[
   a + b + c + d = 360^\circ + 67^\circ = 427^\circ
   \]

Thus, the sum of the angles \(a + b + c + d\) is **427°**, which corresponds to option **B**.

---

Do you have any questions or need further explanation?

### Related Questions:
1. What is the sum of the interior angles of a triangle?
2. How do you calculate the sum of exterior angles for any polygon?
3. Why is the sum of exterior angles always \(360^\circ\)?
4. How are supplementary angles related to exterior angles?
5. Can the sum of interior angles help determine unknown exterior angles?

**Tip:** When working with triangles, always remember that the sum of the interior angles is \(180^\circ\), and the sum of exterior angles for any polygon is always \(360^\circ\).

Halle la suma de los ángulos a + b + c + d.

Solve the problem of finding the sum of angles a + b + c + d in a triangle, using the concepts of exterior and interior angles. This step-by-step guide explains how to apply the sum of exterior angles theorem and calculate supplementary angles. Suitable for students in Grades 9-10.

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