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

Options

A. `30^(@),80^(@),75^(@)`
B. `45^(@),65^(@),65^(@)`
C. `95^(@),20^(@),68^(@)`
D. `90^(@),45^(@),45^(@)`

Answer

To determine which set of angles can form a triangle, we need to use the fundamental property that the sum of the angles in a triangle must equal 180 degrees. Let's evaluate each option step by step.

### Step-by-Step Solution:

1. **Option 1: 30°, 80°, 75°**
- Calculate the sum:
\[ 30 + 80 + 75 = 185° \]
- Since 185° is not equal to 180°, this set of angles cannot form a triangle.

2. **Option 2: 45°, 65°, 65°**
- Calculate the sum:
\[ 45 + 65 + 65 = 175° \]
- Since 175° is not equal to 180°, this set of angles cannot form a triangle.

3. **Option 3: 95°, 20°, 68°**
- Calculate the sum:
\[ 95 + 20 + 68 = 183° \]
- Since 183° is not equal to 180°, this set of angles cannot form a triangle.

4. **Option 4: 90°, 45°, 45°**
- Calculate the sum:
\[ 90 + 45 + 45 = 180° \]
- Since 180° is equal to 180°, this set of angles can form a triangle.

### Conclusion:
The only set of angles that can form a triangle is **Option 4: 90°, 45°, 45°**.