One of the angle of a parallelogram is `4/(5)` of its adjacent angle. Find the measure of both angles.

Answer

To solve the problem, we need to find the measures of the two adjacent angles of a parallelogram, where one angle is \( \frac{4}{5} \) of its adjacent angle.

### Step-by-step Solution:

1. **Define the angles**:
Let one angle of the parallelogram be \( x \) degrees. The adjacent angle will then be \( \frac{4}{5}x \) degrees.

2. **Use the property of parallelograms**:
The sum of two adjacent angles in a parallelogram is always \( 180^\circ \). Therefore, we can set up the equation:
\[ x + \frac{4}{5}x = 180 \]

3. **Combine the terms**:
To combine the terms on the left side, we can express \( x \) as \( \frac{5}{5}x \):
\[ \frac{5}{5}x + \frac{4}{5}x = 180 \]
This simplifies to:
\[ \frac{9}{5}x = 180 \]

4. **Solve for \( x \)**:
To isolate \( x \), multiply both sides by \( \frac{5}{9} \):
\[ x = 180 \times \frac{5}{9} \]
Calculating this gives:
\[ x = 100 \text{ degrees} \]

5. **Find the adjacent angle**:
Now that we have \( x \), we can find the adjacent angle:
\[ \text{Adjacent angle} = \frac{4}{5}x = \frac{4}{5} \times 100 = 80 \text{ degrees} \]

6. **Conclusion**:
The measures of the two angles in the parallelogram are:
- One angle: \( 100^\circ \)
- Adjacent angle: \( 80^\circ \)

### Final Answer:
The two angles of the parallelogram are \( 100^\circ \) and \( 80^\circ \).

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