Two angles of a triangle are `58^(@) and 44^(@)`. Find the third angle.

Options

A. `89^(@)`
B. `68^(@)`
C. `76^(@)`
D. `78^(@)`

Answer

To find the third angle of a triangle when two angles are given, we can use the angle sum property of triangles, which states that the sum of all angles in a triangle is always 180 degrees.

### Step-by-Step Solution:

1. **Identify the given angles**:
- Let angle A = 58 degrees
- Let angle B = 44 degrees

2. **Use the angle sum property**:
- According to the angle sum property, the sum of the angles in a triangle is 180 degrees.
- Therefore, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]

3. **Substitute the known values**:
- Substitute the values of angle A and angle B into the equation:
\[ 58^\circ + 44^\circ + \text{Angle C} = 180^\circ \]

4. **Calculate the sum of angle A and angle B**:
- Add 58 degrees and 44 degrees:
\[ 58^\circ + 44^\circ = 102^\circ \]

5. **Set up the equation to find angle C**:
- Now substitute the sum back into the equation:
\[ 102^\circ + \text{Angle C} = 180^\circ \]

6. **Isolate angle C**:
- To find angle C, subtract 102 degrees from both sides:
\[ \text{Angle C} = 180^\circ - 102^\circ \]

7. **Perform the subtraction**:
- Calculate:
\[ \text{Angle C} = 78^\circ \]

8. **Conclusion**:
- Thus, the third angle of the triangle is:
\[ \text{Angle C} = 78^\circ \]

### Final Answer:
The third angle of the triangle is **78 degrees**.