The measures of two angles of a triangle are `72^(@)` and `58^(@)`. Find the measure of the third angle.

Answer

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

### Step-by-Step Solution:

1. **Understand the Triangle Angle Sum Property**:
The sum of all angles in a triangle is always 180 degrees. This can be expressed as:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]

2. **Identify the Given Angles**:
We have two angles:
- Angle A = 72 degrees
- Angle B = 58 degrees

3. **Set Up the Equation**:
Let Angle C be the measure of the third angle. We can write the equation as:
\[ 72^\circ + 58^\circ + \text{Angle C} = 180^\circ \]

4. **Combine the Known Angles**:
First, we need to add the measures of Angle A and Angle B:
\[ 72^\circ + 58^\circ = 130^\circ \]

5. **Substitute and Solve for Angle C**:
Now, substitute the sum of the known angles back into the equation:
\[ 130^\circ + \text{Angle C} = 180^\circ \]
To find Angle C, subtract 130 degrees from both sides:
\[ \text{Angle C} = 180^\circ - 130^\circ \]
\[ \text{Angle C} = 50^\circ \]

6. **Conclusion**:
The measure of the third angle is:
\[ \text{Angle C} = 50^\circ \]