In a `triangleABC, angleA=35^(@)` and `angleB=65^(@)`,find the measure of `angleC`

Options

A. `80^(@)`
B. `120^(@)`
C. `155^(@)`
D. `140^(@)`

Answer

To find the measure of angle C in triangle ABC where angle A = 35° and angle B = 65°, we can follow these steps:

### Step-by-Step Solution:

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

2. **Substitute the Known Values**:
We know the measures of angle A and angle B:
\[ \text{angle A} = 35° \quad \text{and} \quad \text{angle B} = 65° \]
Substitute these values into the triangle angle sum equation:
\[ 35° + 65° + \text{angle C} = 180° \]

3. **Calculate the Sum of Angles A and B**:
First, add angle A and angle B together:
\[ 35° + 65° = 100° \]

4. **Set Up the Equation for Angle C**:
Now, substitute the sum back into the equation:
\[ 100° + \text{angle C} = 180° \]

5. **Isolate Angle C**:
To find angle C, subtract 100° from both sides of the equation:
\[ \text{angle C} = 180° - 100° \]

6. **Calculate Angle C**:
Now perform the subtraction:
\[ \text{angle C} = 80° \]

### Final Answer:
The measure of angle C is **80°**.

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