Two angles of a triangle are `1/2` radian and `1/3` radian. The measure of the third angle in degree (taking `pi` = `22/7`)

Options

A. `132 "" (1)/(11)""^(@)`
B. `132"" (2)/(11)""^(@)`
C. `132"" (3)/(11)""^(@)`
D. `132^(@)`

Answer

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

### Step-by-Step Solution:

1. **Identify the Given Angles**:
The two angles of the triangle are:
- Angle A = \( \frac{1}{2} \) radian
- Angle B = \( \frac{1}{3} \) radian

2. **Convert Radians to Degrees**:
We know that \( 1 \) radian = \( \frac{180}{\pi} \) degrees. We will use \( \pi = \frac{22}{7} \) as given in the problem.

- For Angle A:
\[ A_{degrees} = \frac{1}{2} \times \frac{180}{\pi} = \frac{1}{2} \times \frac{180 \times 7}{22} = \frac{90 \times 7}{22} = \frac{630}{22} = \frac{315}{11} \text{ degrees} \]

- For Angle B:
\[ B_{degrees} = \frac{1}{3} \times \frac{180}{\pi} = \frac{1}{3} \times \frac{180 \times 7}{22} = \frac{60 \times 7}{22} = \frac{420}{22} = \frac{210}{11} \text{ degrees} \]

3. **Calculate the Third Angle**:
The sum of the angles in a triangle is \( 180 \) degrees. Let the third angle be \( C \).

\[ A_{degrees} + B_{degrees} + C = 180 \]
\[ \frac{315}{11} + \frac{210}{11} + C = 180 \]
\[ \frac{525}{11} + C = 180 \]
\[ C = 180 - \frac{525}{11} \]

To perform this subtraction, convert \( 180 \) into a fraction with a denominator of \( 11 \):
\[ 180 = \frac{180 \times 11}{11} = \frac{1980}{11} \]
Now, substituting back:
\[ C = \frac{1980}{11} - \frac{525}{11} = \frac{1980 - 525}{11} = \frac{1455}{11} \text{ degrees} \]

4. **Final Calculation**:
Now, we can simplify \( \frac{1455}{11} \):
\[ C = 132 \frac{3}{11} \text{ degrees} \]

### Conclusion:
The measure of the third angle in degrees is \( 132 \frac{3}{11} \) degrees.

---