Find the third angle of a triangle, two of whose angles are `65^(@) and 71^(@)`.

Options

A. `84^(@)`.
B. `54^(@)`.
C. `44^(@)`.
D. `64^(@)`.

Answer

To find the third angle of a triangle when two angles are given, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given angles**:
- Angle A = 65 degrees
- Angle B = 71 degrees

2. **Use the triangle angle sum property**:
- The sum of all angles in a triangle is always 180 degrees. This can be expressed as:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]

3. **Substitute the known values into the equation**:
- Substitute Angle A and Angle B into the equation:
\[ 65^\circ + 71^\circ + \text{Angle C} = 180^\circ \]

4. **Combine the known angles**:
- Add 65 and 71:
\[ 65 + 71 = 136 \]
- Now the equation becomes:
\[ 136^\circ + \text{Angle C} = 180^\circ \]

5. **Solve for Angle C**:
- To find Angle C, subtract 136 degrees from 180 degrees:
\[ \text{Angle C} = 180^\circ - 136^\circ = 44^\circ \]

6. **Conclusion**:
- Therefore, the third angle (Angle C) is 44 degrees.

### Final Answer:
The third angle of the triangle is **44 degrees**.