If the angles of a triangle ABC are in the ratio 2 : 3 : 1, then the angles, `/_A, /_B and /_C` are

Options

A. `/_A = 60^@, /_B = 90^@, /_C = 30^@`
B. `/_A = 40^@, /_B = 120^@, /_C = 20^@`
C. `/_A = 20^@, /_B = 90^@, /_C = 60^@`
D. `/_A = 45^@, /_B = 70^@, /_C = 45^@`

Answer

To find the angles of triangle ABC given that they are in the ratio 2:3:1, we can follow these steps:

### Step 1: Define the angles in terms of a variable
Let the angles of triangle ABC be represented as:
- Angle A = 2k
- Angle B = 3k
- Angle C = k

### Step 2: Use the property of the sum of angles in a triangle
We know that the sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
\[ 2k + 3k + k = 180 \]

### Step 3: Combine like terms
Combine the terms on the left side of the equation:
\[ (2k + 3k + k) = 6k \]
So, we have:
\[ 6k = 180 \]

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

### Step 5: Calculate each angle
Now that we have the value of k, we can find each angle:
- Angle A = 2k = 2 × 30 = 60 degrees
- Angle B = 3k = 3 × 30 = 90 degrees
- Angle C = k = 30 degrees

### Conclusion
Thus, the angles of triangle ABC are:
- Angle A = 60 degrees
- Angle B = 90 degrees
- Angle C = 30 degrees