The angles of a triangle are in the ratio 2:3: 7. The measure of the largest angle is

Options

A. `84^(@)`
B. `98^(@)`
C. `105^(@)`
D. `91^(@)`

Answer

To find the measure of the largest angle in a triangle where the angles are in the ratio 2:3:7, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio of Angles**:
The angles of the triangle are given in the ratio 2:3:7. This means we can express the angles in terms of a variable \( x \).
- Let the angles be \( 2x \), \( 3x \), and \( 7x \).

2. **Use the Sum of Angles in a Triangle**:
We know that the sum of the angles in a triangle is always \( 180^\circ \).
- Therefore, we can write the equation:
\[ 2x + 3x + 7x = 180^\circ \]

3. **Combine Like Terms**:
Combine the terms on the left side of the equation:
\[ (2 + 3 + 7)x = 180^\circ \]
This simplifies to:
\[ 12x = 180^\circ \]

4. **Solve for \( x \)**:
To find the value of \( x \), divide both sides of the equation by 12:
\[ x = \frac{180^\circ}{12} = 15^\circ \]

5. **Calculate Each Angle**:
Now that we have \( x \), we can find each angle:
- First angle: \( 2x = 2 \times 15^\circ = 30^\circ \)
- Second angle: \( 3x = 3 \times 15^\circ = 45^\circ \)
- Third angle: \( 7x = 7 \times 15^\circ = 105^\circ \)

6. **Identify the Largest Angle**:
Among the angles \( 30^\circ \), \( 45^\circ \), and \( 105^\circ \), the largest angle is:
\[ 105^\circ \]

### Final Answer:
The measure of the largest angle is \( 105^\circ \).

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