The angles of a triangle are `(3x)^(@)`, `(2x-7)^(@)` and `(4x-11)^(@)`. Then, x = ?

Options

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

Answer

To solve for \( x \) in the triangle with angles \( 3x \), \( 2x - 7 \), and \( 4x - 11 \), 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 \( 180^\circ \). Therefore, we can write the equation:

\[ 3x + (2x - 7) + (4x - 11) = 180 \]

### Step 2: Simplify the equation
Combine like terms on the left side of the equation:

\[ 3x + 2x + 4x - 7 - 11 = 180 \]

This simplifies to:

\[ (3x + 2x + 4x) + (-7 - 11) = 180 \]

\[ 9x - 18 = 180 \]

### Step 3: Isolate \( x \)
Now, add \( 18 \) to both sides of the equation to isolate the term with \( x \):

\[ 9x - 18 + 18 = 180 + 18 \]

This simplifies to:

\[ 9x = 198 \]

### Step 4: Solve for \( x \)
Now, divide both sides by \( 9 \) to find \( x \):

\[ x = \frac{198}{9} \]

Calculating the division gives:

\[ x = 22 \]

### Final Answer:
Thus, the value of \( x \) is \( 22 \).

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