Construct a parallelogram ABCD where AB=4.2cm, AD=3.5 cm and `/_A=75^(@)`

Answer

To construct a parallelogram ABCD where AB = 4.2 cm, AD = 3.5 cm, and angle A = 75°, follow these steps:

### Step-by-Step Solution:

1. **Draw Line Segment AB**:
- Using a ruler, draw a line segment AB measuring 4.2 cm. Label the endpoints as A and B.
- **Hint**: Make sure to measure accurately using the ruler to get the correct length.

2. **Construct Angle A**:
- At point A, use a protractor to measure an angle of 75°. Draw a ray from point A at this angle. Label the point where the ray extends as point D.
- **Hint**: Ensure the protractor is aligned correctly with line AB to measure the angle accurately.

3. **Measure Length AD**:
- Using a compass, set the width to 3.5 cm. Place the compass point on A and draw an arc across the ray AD. This arc will help locate point D.
- **Hint**: Keep the compass steady while drawing the arc to maintain the correct distance.

4. **Locate Point D**:
- Mark the intersection of the arc with the ray AD as point D. Now you have points A and D.
- **Hint**: Ensure that the point D is on the ray you drew at 75° from point A.

5. **Construct Angle B**:
- At point B, use a protractor to measure an angle of 105° (since angle B is supplementary to angle A). Draw a ray from point B at this angle.
- **Hint**: Double-check the angle measurement to ensure accuracy.

6. **Measure Length BC**:
- Set the compass to 4.2 cm (the same length as AB) and place the compass point on B. Draw an arc that intersects the ray you drew from B. Label the intersection point as C.
- **Hint**: Make sure the compass width remains constant while drawing the arc.

7. **Complete the Parallelogram**:
- Connect points C and D with a straight line. Now you have the parallelogram ABCD.
- **Hint**: Use a ruler to draw the line accurately between points C and D.

### Final Check:
- Verify that AB = CD = 4.2 cm and AD = BC = 3.5 cm.
- Check that angles A and B are 75° and 105°, respectively.