If the measures of a quadrilateral are `(6x)^(@)` , `5(x+2)^(@) , (7x-20)^(@)` and `2(2x + 9)^(@)` respectively, then the value of x is

Options

A. `10^(@)`
B. `16^(@)`
C. `30^(@)`
D. `32^(@)`

Answer

To find the value of \( x \) in the given quadrilateral with angles \( (6x)^\circ \), \( 5(x+2)^\circ \), \( (7x-20)^\circ \), and \( 2(2x + 9)^\circ \), we will follow these steps:

### Step 1: Write the equation for the sum of angles in a quadrilateral.
The sum of the angles in a quadrilateral is always \( 360^\circ \). Therefore, we can set up the equation:
\[ (6x) + 5(x + 2) + (7x - 20) + 2(2x + 9) = 360 \]

### Step 2: Expand and simplify the equation.
Now, we will expand the terms:
\[ 6x + 5x + 10 + 7x - 20 + 4x + 18 = 360 \]
Combine like terms:
\[ (6x + 5x + 7x + 4x) + (10 - 20 + 18) = 360 \]
This simplifies to:
\[ 22x + 8 = 360 \]

### Step 3: Isolate \( x \).
Next, we will isolate \( x \) by subtracting 8 from both sides:
\[ 22x = 360 - 8 \]
\[ 22x = 352 \]

### Step 4: Solve for \( x \).
Now, divide both sides by 22:
\[ x = \frac{352}{22} \]
\[ x = 16 \]

### Conclusion:
Thus, the value of \( x \) is \( 16 \).

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