Two adjacent angles of a parallelogram are `(2x + 25)^(@) and (3x - 5)^(@)` . The value of x is

Options

A. `28^(@)`
B. `32^(@)`
C. `36^(@)`
D. `42^(@)`

Answer

To find the value of \( x \) in the given problem, we follow these steps:

### Step 1: Write down the expressions for the angles.
We are given two adjacent angles of a parallelogram:
- Angle 1: \( (2x + 25)^\circ \)
- Angle 2: \( (3x - 5)^\circ \)

### Step 2: Use the property of adjacent angles in a parallelogram.
In a parallelogram, the sum of adjacent angles is equal to \( 180^\circ \). Therefore, we can write the equation:
\[ (2x + 25) + (3x - 5) = 180 \]

### Step 3: Simplify the equation.
Combine like terms:
\[ 2x + 25 + 3x - 5 = 180 \]
This simplifies to:
\[ (2x + 3x) + (25 - 5) = 180 \]
\[ 5x + 20 = 180 \]

### Step 4: Solve for \( x \).
To isolate \( x \), subtract 20 from both sides:
\[ 5x = 180 - 20 \]
\[ 5x = 160 \]
Now, divide both sides by 5:
\[ x = \frac{160}{5} \]
\[ x = 32 \]

### Conclusion:
The value of \( x \) is \( 32 \).

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