In `/_\\ABC, if /_A =65^(@)` and `/_C =85^(@)`, then `/_`B = ?

Options

A. `25^(@)`
B. `30^(@)`
C. `35^(@)`
D. `40^(@)`

Answer

To find the measure of angle B in triangle ABC, we can use the property that the sum of the angles in a triangle is always equal to 180 degrees.

### Step-by-Step Solution:

1. **Identify the known angles**:
- Angle A = 65 degrees
- Angle C = 85 degrees

2. **Use the triangle angle sum property**:
- The sum of angles in triangle ABC can be expressed as:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]
- Substituting the known values:
\[ 65^\circ + \text{Angle B} + 85^\circ = 180^\circ \]

3. **Combine the known angles**:
- Add the values of angle A and angle C:
\[ 65^\circ + 85^\circ = 150^\circ \]
- Now the equation becomes:
\[ 150^\circ + \text{Angle B} = 180^\circ \]

4. **Isolate angle B**:
- To find angle B, subtract 150 degrees from both sides:
\[ \text{Angle B} = 180^\circ - 150^\circ \]

5. **Calculate angle B**:
- Performing the subtraction:
\[ \text{Angle B} = 30^\circ \]

### Final Answer:
\[ \text{Angle B} = 30^\circ \]