The angles of a triangle are `(3x)^(0)(2x-7)^(0) and (4x-11)^(0)`. The value of x is

Options

A. 18
B. 20
C. 22
D. 30

Answer

To find the value of \( x \) in the triangle with angles \( 3x^\circ \), \( (2x - 7)^\circ \), and \( (4x - 11)^\circ \), we can follow these steps:

### Step 1: Set up the equation using the triangle angle sum property
The sum of the angles in a triangle is always equal to \( 180^\circ \). Therefore, we can write the equation:
\[ 3x + (2x - 7) + (4x - 11) = 180 \]

### Step 2: Simplify the equation
Combine like terms:
\[ 3x + 2x + 4x - 7 - 11 = 180 \]
This simplifies to:
\[ (3x + 2x + 4x) + (-7 - 11) = 180 \]
\[ 9x - 18 = 180 \]

### Step 3: Solve for \( x \)
Now, isolate \( x \) by adding \( 18 \) to both sides:
\[ 9x = 180 + 18 \]
\[ 9x = 198 \]
Next, divide both sides by \( 9 \):
\[ x = \frac{198}{9} \]
\[ x = 22 \]

### Conclusion
The value of \( x \) is \( 22 \).

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