If the sides of a triangle are extended in both the sides then the sum of the exterior angles so formed in both sides is

Options

A. `360^@`
B. `540^@`
C. `720^@`
D. `180^@`

Answer

To solve the problem of finding the sum of the exterior angles formed when the sides of a triangle are extended on both sides, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Exterior Angles**:
- An exterior angle is formed when a side of a triangle is extended. For each vertex of the triangle, there is one exterior angle corresponding to the angle at that vertex.

2. **Identifying the Triangle**:
- Let’s denote the triangle as ABC, where A, B, and C are the vertices of the triangle.

3. **Calculating Exterior Angles**:
- For each vertex, the exterior angle can be calculated as follows:
- Exterior angle at vertex A = 180° - angle A
- Exterior angle at vertex B = 180° - angle B
- Exterior angle at vertex C = 180° - angle C

4. **Sum of Exterior Angles**:
- The sum of the exterior angles for triangle ABC is:
\[ (180° - A) + (180° - B) + (180° - C) \]
- Simplifying this, we get:
\[ 180° + 180° + 180° - (A + B + C) \]
- Since the sum of the interior angles of a triangle is always 180° (i.e., A + B + C = 180°), we can substitute:
\[ 540° - 180° = 360° \]

5. **Considering Both Sides**:
- Since the question asks for the sum of the exterior angles formed on both sides of the triangle, we need to double the sum we just calculated:
\[ 2 \times 360° = 720° \]

### Final Answer:
The sum of the exterior angles formed when the sides of a triangle are extended on both sides is **720°**.

---