In a △ABC it is given that `/_B = 37^(@)`  and `/_C =29^(@)` . Then, `/_A `= ?

Options

A. `86^(@)`
B. `66^(@)`
C. `114^(@)`
D. `57^(@)`

Answer

To find the measure of angle A in triangle ABC, we can use the property that the sum of the angles in a triangle is always equal to 180 degrees. Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Identify the given angles**:
- Angle B = 37 degrees
- Angle C = 29 degrees

2. **Write the equation for the sum of angles in a triangle**:
- According to the triangle angle sum property, we have:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]

3. **Substitute the known values into the equation**:
- Substitute the values of Angle B and Angle C into the equation:
\[ \text{Angle A} + 37^\circ + 29^\circ = 180^\circ \]

4. **Combine the known angles**:
- Add the measures of Angle B and Angle C:
\[ 37^\circ + 29^\circ = 66^\circ \]
- Now the equation becomes:
\[ \text{Angle A} + 66^\circ = 180^\circ \]

5. **Isolate Angle A**:
- To find Angle A, subtract 66 degrees from both sides:
\[ \text{Angle A} = 180^\circ - 66^\circ \]

6. **Calculate the value of Angle A**:
- Perform the subtraction:
\[ \text{Angle A} = 114^\circ \]

### Final Answer:
- Angle A = 114 degrees