Two adjacent angles in a parallelogram are in the ratio `2:4`. The values of angles are

Options

A. `80^(@), 100^(@)`
B. `40^(@), 140^(@)`
C. `60^(@), 120^(@)`
D. `70^(@), 140^(@)`

Answer

To solve the problem, we need to find the values of two adjacent angles in a parallelogram that are in the ratio of 2:4.

### Step-by-Step Solution:

1. **Define the Angles**:
Let the two adjacent angles be represented as \(2x\) and \(4x\).

2. **Use the Property of Parallelograms**:
In a parallelogram, adjacent angles are supplementary. This means their sum is equal to \(180^\circ\). Therefore, we can write the equation:
\[ 2x + 4x = 180^\circ \]

3. **Combine Like Terms**:
Combine the terms on the left side of the equation:
\[ 6x = 180^\circ \]

4. **Solve for \(x\)**:
Divide both sides of the equation by 6 to find the value of \(x\):
\[ x = \frac{180^\circ}{6} = 30^\circ \]

5. **Find the Angles**:
Now, substitute the value of \(x\) back into the expressions for the angles:
- First angle:
\[ 2x = 2 \times 30^\circ = 60^\circ \]
- Second angle:
\[ 4x = 4 \times 30^\circ = 120^\circ \]

6. **Conclusion**:
The values of the two adjacent angles in the parallelogram are \(60^\circ\) and \(120^\circ\).

### Final Answer:
The values of the angles are \(60^\circ\) and \(120^\circ\).

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