Which of the following set of angles can form a triangle ?

Options

A. `70^(@), 90^(@), 25^(@)`
B. `65^(@), 85^(@), 40^(@)`
C. `65^(@), 85^(@), 30^(@)`
D. `45^(@), 45^(@), 80^(@)`

Answer

To determine which set of angles can form a triangle, we need to check if the sum of the angles in each option equals 180 degrees.

### Step-by-Step Solution:

1. **Understand the Triangle Angle Sum Property**:
The sum of the angles in a triangle must equal 180 degrees.

2. **Check Each Option**:
- **Option 1**: Angles = 70°, 90°, 25°
- Calculate the sum:
\[ 70 + 90 + 25 = 185 \text{ degrees} \]
- Since 185° is not equal to 180°, this option cannot form a triangle.

- **Option 2**: Angles = 65°, 85°, 40°
- Calculate the sum:
\[ 65 + 85 + 40 = 190 \text{ degrees} \]
- Since 190° is not equal to 180°, this option cannot form a triangle.

- **Option 3**: Angles = 65°, 85°, 30°
- Calculate the sum:
\[ 65 + 85 + 30 = 180 \text{ degrees} \]
- Since 180° is equal to 180°, this option can form a triangle.

- **Option 4**: Angles = 45°, 45°, 80°
- Calculate the sum:
\[ 45 + 45 + 80 = 170 \text{ degrees} \]
- Since 170° is not equal to 180°, this option cannot form a triangle.

3. **Conclusion**:
The only set of angles that can form a triangle is **Option 3: 65°, 85°, and 30°**.