Construct a quadrilateral ABCD in which AB=4cm, BC=6cm, CD=6cm, `/_B=120^(@)` and `/_C=90^(@)`.

Answer

To construct the quadrilateral ABCD with the given dimensions and angles, follow these steps:

### Step-by-Step Construction:

1. **Draw Line Segment AB:**
- Draw a line segment AB measuring 4 cm.
- Mark point A on one end and point B on the other end.

**Hint:** Use a ruler to measure the length accurately.

2. **Construct Angle B:**
- At point B, use a protractor to measure and construct an angle of 120°.
- Draw a ray from point B in the direction of the 120° angle.

**Hint:** Ensure the protractor's center is at point B for accurate measurement.

3. **Mark Point C:**
- From point B, measure 6 cm along the ray you just drew and mark this point as C.

**Hint:** Use a compass or ruler to ensure the length is exactly 6 cm.

4. **Construct Angle C:**
- At point C, use a protractor to construct a right angle (90°).
- Draw a ray from point C in the direction of the 90° angle.

**Hint:** Make sure the ray is perpendicular to line segment BC.

5. **Mark Point D:**
- From point C, measure 6 cm along the ray you just drew and mark this point as D.

**Hint:** Again, use a compass or ruler to ensure the length is exactly 6 cm.

6. **Complete the Quadrilateral:**
- Finally, connect points A and D with a straight line to complete the quadrilateral ABCD.

**Hint:** Ensure that the lines are straight and connect the points accurately.

### Summary of the Construction:
- You have constructed a quadrilateral ABCD where:
- AB = 4 cm
- BC = 6 cm
- CD = 6 cm
- ∠B = 120°
- ∠C = 90°