Find the other angles of a parallelogram if its one angle is `60^(@)`

Answer

To find the other 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**:
Let the parallelogram be \(ABCD\) and we know that one angle, say \(\angle A\), is \(60^\circ\).

2. **Use the Properties of Parallelograms**:
In a parallelogram, opposite angles are equal. Therefore, if \(\angle A = 60^\circ\), then \(\angle C\) (the angle opposite to \(\angle A\)) is also:
\[ \angle C = 60^\circ \]

3. **Find the Adjacent Angles**:
The sum of the adjacent angles in a parallelogram is \(180^\circ\). Thus, we can write:
\[ \angle A + \angle B = 180^\circ \]
Substituting the value of \(\angle A\):
\[ 60^\circ + \angle B = 180^\circ \]

4. **Solve for \(\angle B\)**:
Rearranging the equation gives:
\[ \angle B = 180^\circ - 60^\circ = 120^\circ \]

5. **Find the Remaining Angle**:
Since \(\angle B\) is \(120^\circ\) and opposite angles are equal, we have:
\[ \angle D = \angle B = 120^\circ \]

6. **Summarize the Angles**:
We have found all angles of the parallelogram:
- \(\angle A = 60^\circ\)
- \(\angle B = 120^\circ\)
- \(\angle C = 60^\circ\)
- \(\angle D = 120^\circ\)

7. **Verify the Sum of Angles**:
To ensure correctness, we can check that the sum of all angles in the parallelogram equals \(360^\circ\):
\[ 60^\circ + 120^\circ + 60^\circ + 120^\circ = 360^\circ \]

### Final Answer:
The angles of the parallelogram are:
- \(\angle A = 60^\circ\)
- \(\angle B = 120^\circ\)
- \(\angle C = 60^\circ\)
- \(\angle D = 120^\circ\)