In a parallelogram, one angleis twice of its consecutiv angle. Find all the angles of the parallelogram.

Answer

To find all the angles of a parallelogram where one angle is twice its consecutive angle, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Angles**:
Let one angle of the parallelogram be \( x \). According to the problem, the consecutive angle will then be \( 2x \).

2. **Identify Opposite Angles**:
In a parallelogram, opposite angles are equal. Therefore, if one angle is \( x \), the opposite angle will also be \( x \). Similarly, if one angle is \( 2x \), the opposite angle will also be \( 2x \).

3. **Set Up the Equation**:
The sum of all angles in a quadrilateral (which includes parallelograms) is \( 360^\circ \). Therefore, we can write the equation:
\[ x + 2x + x + 2x = 360^\circ \]

4. **Combine Like Terms**:
Simplifying the left side of the equation gives:
\[ 6x = 360^\circ \]

5. **Solve for \( x \)**:
To find \( x \), divide both sides of the equation by 6:
\[ x = \frac{360^\circ}{6} = 60^\circ \]

6. **Find the Other Angle**:
Now that we have \( x \), we can find \( 2x \):
\[ 2x = 2 \times 60^\circ = 120^\circ \]

7. **List All Angles**:
The angles of the parallelogram are:
- \( x = 60^\circ \)
- \( 2x = 120^\circ \)
- The opposite angles are also \( 60^\circ \) and \( 120^\circ \).

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

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