Assertion : Two opposite angles of a parallelogram are `(3x-2)^(@) and (50 - x)^(@)` . The measure of one of the angle is `37^(@)` .
Reason : Opposite angles of a parallelogram are equal

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the problem, we need to verify the assertion and reason given in the question regarding the angles of a parallelogram.

### Step 1: Understand the properties of a parallelogram
In a parallelogram, opposite angles are equal. This means if we have angles A and C as opposite angles, then:
\[ \text{Angle A} = \text{Angle C} \]
Similarly, for angles B and D:
\[ \text{Angle B} = \text{Angle D} \]

### Step 2: Set up the equations based on the assertion
According to the assertion, we have two opposite angles given as:
- Angle A = \( (3x - 2)^\circ \)
- Angle C = \( (50 - x)^\circ \)

Since these angles are opposite angles in a parallelogram, we can set them equal to each other:
\[ 3x - 2 = 50 - x \]

### Step 3: Solve for x
To solve for \( x \), we will rearrange the equation:
1. Add \( x \) to both sides:
\[ 3x + x - 2 = 50 \]
\[ 4x - 2 = 50 \]

2. Next, add 2 to both sides:
\[ 4x = 52 \]

3. Now, divide both sides by 4:
\[ x = 13 \]

### Step 4: Find the measure of the angles
Now that we have the value of \( x \), we can find the measure of one of the angles. Let's substitute \( x \) back into the expression for Angle A:
\[ \text{Angle A} = 3x - 2 = 3(13) - 2 = 39 - 2 = 37^\circ \]

### Step 5: Verify the assertion
The problem states that one of the angles is \( 37^\circ \). We have calculated Angle A to be \( 37^\circ \), which confirms the assertion is true.

### Step 6: Conclusion
Since we have verified that the assertion is true and the reason (that opposite angles in a parallelogram are equal) is also true, we conclude that both the assertion and reason are correct.