Two adjacent angles of a parallelograms 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 will follow these steps:

### Step 1: Set up the equation
We know that the sum of two adjacent angles in a parallelogram is \( 180^\circ \). The two angles given are \( (2x + 25)^\circ \) and \( (3x - 5)^\circ \). Therefore, we can write the equation:
\[ (2x + 25) + (3x - 5) = 180 \]

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

### Step 3: Isolate the variable \( x \)
Next, we will isolate \( x \) by subtracting \( 20 \) from both sides of the equation:
\[ 5x = 180 - 20 \]
\[ 5x = 160 \]

### Step 4: Solve for \( x \)
Now, divide both sides by \( 5 \) to find \( x \):
\[ x = \frac{160}{5} \]
Calculating this gives:
\[ x = 32 \]

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

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