If the angles of a triangle are `(2x -8)^@, (2x + 18)^@` and `6x^@`, what is the value of 3x (in degrees)?

Options

A. `17`
B. `34`
C. `51`
D. `60`

Answer

To solve the problem, we need to find the value of \(3x\) given the angles of a triangle as \((2x - 8)^\circ\), \((2x + 18)^\circ\), and \(6x^\circ\).

### Step-by-Step Solution:

1. **Write the equation for the sum of angles in a triangle**:
The sum of the angles in a triangle is always \(180^\circ\). Therefore, we can set up the equation:
\[ (2x - 8) + (2x + 18) + 6x = 180 \]

2. **Combine like terms**:
Combine the terms on the left side of the equation:
\[ 2x - 8 + 2x + 18 + 6x = 180 \]
This simplifies to:
\[ (2x + 2x + 6x) + (-8 + 18) = 180 \]
Which further simplifies to:
\[ 10x + 10 = 180 \]

3. **Isolate \(x\)**:
To solve for \(x\), subtract \(10\) from both sides:
\[ 10x = 180 - 10 \]
This gives:
\[ 10x = 170 \]

4. **Divide by 10**:
Now, divide both sides by \(10\) to find \(x\):
\[ x = \frac{170}{10} = 17 \]

5. **Calculate \(3x\)**:
Now that we have \(x\), we can find \(3x\):
\[ 3x = 3 \times 17 = 51 \]

### Final Answer:
The value of \(3x\) is \(51^\circ\).

---