Two adjacent angles of a parallelogram are in the ratio 2 : 3. The angles are

Options

A. `90^(@),180^(@)`
B. `36^(@),144^(@)`
C. `72^(@),108^(@)`
D. `52^(@),104^(@)`

Answer

To solve the problem of finding the two adjacent angles of a parallelogram that are in the ratio of 2:3, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Properties of a Parallelogram**:
In a parallelogram, the sum of two adjacent angles is always 180 degrees.

2. **Setting Up the Angles**:
Let the two adjacent angles be represented as:
- Angle A = 2x
- Angle B = 3x
Here, we are using the ratio 2:3.

3. **Applying the Property of the Parallelogram**:
According to the property mentioned, we can write the equation:
\[ \text{Angle A} + \text{Angle B} = 180^\circ \]
Substituting the expressions for Angle A and Angle B, we get:
\[ 2x + 3x = 180^\circ \]

4. **Combining Like Terms**:
Combine the terms on the left side:
\[ 5x = 180^\circ \]

5. **Solving for x**:
To find the value of x, divide both sides by 5:
\[ x = \frac{180^\circ}{5} = 36^\circ \]

6. **Finding the Angles**:
Now, substitute the value of x back into the expressions for Angle A and Angle B:
- Angle A = \(2x = 2 \times 36^\circ = 72^\circ\)
- Angle B = \(3x = 3 \times 36^\circ = 108^\circ\)

7. **Conclusion**:
The two adjacent angles of the parallelogram are:
- Angle A = 72 degrees
- Angle B = 108 degrees

### Final Answer:
The angles are 72 degrees and 108 degrees.

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