The angles of a triangle are in the ratio 3: 1:2. The measure of the largest angle is

Options

A. `30^(@)`
B. `60^(@)`
C. `90^(@)`
D. `120^(@)`

Answer

To find the measure of the largest angle in a triangle where the angles are in the ratio 3:1:2, 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 3:1:2. This means we can represent the angles as:
- Angle A = 3x
- Angle B = 1x
- Angle C = 2x

2. **Set Up the Equation**:
The sum of the angles in any triangle is always 180 degrees. Therefore, we can write the equation:
\[ Angle A + Angle B + Angle C = 180 \]
Substituting the expressions for the angles, we have:
\[ 3x + 1x + 2x = 180 \]

3. **Combine Like Terms**:
Combine the terms on the left side of the equation:
\[ (3x + 1x + 2x) = 6x \]
So, the equation now is:
\[ 6x = 180 \]

4. **Solve for x**:
To find the value of x, divide both sides of the equation by 6:
\[ x = \frac{180}{6} = 30 \]

5. **Calculate Each Angle**:
Now that we have the value of x, we can find each angle:
- Angle A = 3x = 3 * 30 = 90 degrees
- Angle B = 1x = 1 * 30 = 30 degrees
- Angle C = 2x = 2 * 30 = 60 degrees

6. **Identify the Largest Angle**:
Among the calculated angles (90 degrees, 30 degrees, and 60 degrees), the largest angle is:
\[ \text{Largest Angle} = 90 \text{ degrees} \]

### Final Answer:
The measure of the largest angle is **90 degrees**.

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