In a `Delta ABC, if angle A = 40^(@) and angle B = 55^(@) " then " angle C ` is

Options

A. `75^(@)`
B. `80^(@)`
C. `95^(@)`
D. `85^(@)`

Answer

To find angle C in triangle ABC where angle A = 40° and angle B = 55°, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Triangle Angle Sum Property**:
The sum of the angles in a triangle is always 180°. This means:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180° \]

2. **Substitute the Known Values**:
We know the values of angle A and angle B:
\[ 40° + 55° + \text{Angle C} = 180° \]

3. **Calculate the Sum of Angle A and Angle B**:
First, add angle A and angle B together:
\[ 40° + 55° = 95° \]

4. **Set Up the Equation for Angle C**:
Now, substitute the sum back into the triangle angle sum equation:
\[ 95° + \text{Angle C} = 180° \]

5. **Isolate Angle C**:
To find angle C, subtract 95° from both sides of the equation:
\[ \text{Angle C} = 180° - 95° \]

6. **Perform the Subtraction**:
Calculate the value of angle C:
\[ \text{Angle C} = 85° \]

### Final Answer:
Therefore, angle C is 85°.