Construct a quadrilateral PQRS in which PQ=4.5cm,`/_PQR=120^(@),QR=3.cm, /_QRS=100^(@)` and `/_QPS=60^(@)`.

Answer

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

### Step-by-Step Solution:

1. **Draw Line Segment PQ:**
- Using a ruler, draw a line segment PQ measuring 4.5 cm. Label the endpoints as P and Q.
- **Hint:** Ensure that you measure accurately using the ruler for precision.

2. **Construct Angle PQR:**
- At point Q, use a protractor to construct an angle of 120 degrees. Mark the angle and draw a ray QR extending from point Q.
- **Hint:** Remember that the angle is measured from the line segment PQ, so align the protractor correctly.

3. **Mark Length QR:**
- Using a compass, measure 3 cm on the ruler. Place the compass point at Q and draw an arc along the ray QR. Label the intersection point as R.
- **Hint:** Make sure the compass is set to exactly 3 cm to ensure accuracy in your construction.

4. **Construct Angle QRS:**
- At point R, construct an angle of 100 degrees using the protractor. Mark this angle and draw a ray RS extending from point R.
- **Hint:** Double-check the angle measurement to ensure it is accurate.

5. **Construct Angle QPS:**
- At point P, construct an angle of 60 degrees using the protractor. Mark this angle and draw a ray PS extending from point P.
- **Hint:** Ensure that the angle is measured correctly from line segment PQ.

6. **Locate Point S:**
- Extend the rays PS and RS until they intersect. Label the intersection point as S.
- **Hint:** The intersection point is crucial as it defines the fourth vertex of the quadrilateral.

7. **Complete the Quadrilateral:**
- Connect the points P, Q, R, and S to form the quadrilateral PQRS.
- **Hint:** Review the shape to ensure all sides and angles correspond to the given measurements.

### Final Check:
- Verify that the lengths PQ, QR, and the angles PQR, QRS, and QPS match the specified measurements.