One angle of a parallelogram is `60^(@).` Find its remaining angles.

Answer

To find the remaining angles of a parallelogram when one angle is given as \(60^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Angle:**
We know that one angle of the parallelogram, say angle \(A\), is \(60^\circ\).

2. **Use the Property of Opposite Angles:**
In a parallelogram, opposite angles are equal. Therefore, if angle \(A = 60^\circ\), then angle \(C\) (which is opposite to angle \(A\)) is also:
\[ \text{Angle } C = 60^\circ \]

3. **Use the Property of Co-Interior Angles:**
The sum of the co-interior angles (angles on the same side of a transversal) is \(180^\circ\). Thus, we can find angle \(D\) using the relationship:
\[ \text{Angle } A + \text{Angle } D = 180^\circ \]
Substituting the value of angle \(A\):
\[ 60^\circ + \text{Angle } D = 180^\circ \]
To find angle \(D\), we rearrange the equation:
\[ \text{Angle } D = 180^\circ - 60^\circ = 120^\circ \]

4. **Find the Remaining Angle:**
Since angle \(B\) is opposite to angle \(D\), we have:
\[ \text{Angle } B = \text{Angle } D = 120^\circ \]

5. **Summarize the Angles:**
Therefore, the angles of the parallelogram are:
- Angle \(A = 60^\circ\)
- Angle \(B = 120^\circ\)
- Angle \(C = 60^\circ\)
- Angle \(D = 120^\circ\)

### Final Answer:
The remaining angles of the parallelogram are \(60^\circ\), \(120^\circ\), \(120^\circ\).

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