One of the angles of a parallelogram is `55^(@)`. The remaining angles are respectively

Options

A. `105^(@), 125^(@), 55^(@)`
B. `125^(@), 55^(@), 125^(@)`
C. `125^(@), 125^(@), 55^(@)`
D. `25^(@), 135^(@), 135^(@)`

Answer

To find the remaining angles of a parallelogram when one of the angles is given as \(55^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Angle**:
- Let’s denote the angles of the parallelogram as \(A\), \(B\), \(C\), and \(D\).
- We are given that one angle, say \(A\), is \(55^\circ\).
\[ A = 55^\circ \]

2. **Use the Property of Opposite Angles**:
- In a parallelogram, opposite angles are equal. Therefore, angle \(C\) will also be \(55^\circ\).
\[ C = 55^\circ \]

3. **Use the Property of Consecutive Angles**:
- Consecutive angles in a parallelogram are supplementary, meaning they add up to \(180^\circ\). Thus, we can find angles \(B\) and \(D\) using angle \(A\):
\[ B + A = 180^\circ \implies B + 55^\circ = 180^\circ \]

4. **Solve for Angle \(B\)**:
- Rearranging the equation gives:
\[ B = 180^\circ - 55^\circ = 125^\circ \]

5. **Find Angle \(D\)**:
- Since angle \(D\) is opposite to angle \(B\), it will also be equal to \(125^\circ\):
\[ D = 125^\circ \]

6. **Summarize the Angles**:
- Therefore, the angles of the parallelogram are:
\[ A = 55^\circ, \quad B = 125^\circ, \quad C = 55^\circ, \quad D = 125^\circ \]

### Final Answer:
The remaining angles of the parallelogram are \(125^\circ\), \(55^\circ\), and \(125^\circ\).

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