Arrange the steps of construction while constructing a quadrilateral PQRS given that PQ = 4.2 cm, PS = 3 cm, QR = 1.5 cm, ` angle P = 60^(@) and angle Q = 75^(@)`
Steps of construction :
Step 1 : With Q as centre and radius 1.5 cm, cut off QR = 1.5 cm along QX
Step 2 : Construct ` angle QPY = 60^(@) ` at P
Step 3 : Join RS
Step 4 : With P as centre and radius 3 cm, cut off PS = 3 cm along PY
Step 5 : Draw PQ = 4.2 cm
Step 6 : Construct ` angle PQX = 75^(@) ` at Q

Options

A. 5, 2, 4, 1, 3, 6
B. 5, 4, 2, 1, 6, 3
C. 5, 2, 4, 6, 1, 3
D. 5, 2, 4, 1, 6, 3

Answer

To construct the quadrilateral PQRS with the given dimensions and angles, we can follow these steps in the correct order:

### Step-by-Step Solution:

1. **Step 5**: Draw a line segment PQ = 4.2 cm.
- Start by drawing a horizontal line segment of length 4.2 cm and label the endpoints as P and Q.

2. **Step 2**: Construct angle QPY = 60° at point P.
- Use a protractor to measure and construct an angle of 60° at point P, extending the line from P to form ray PY.

3. **Step 4**: With P as the center and radius 3 cm, cut off PS = 3 cm along ray PY.
- Place the compass point at P, adjust it to a radius of 3 cm, and draw an arc along ray PY. Mark the intersection point as S.

4. **Step 6**: Construct angle PQX = 75° at point Q.
- At point Q, use a protractor to measure and construct an angle of 75° on the opposite side of line PQ, extending the line to form ray QX.

5. **Step 1**: With Q as the center and radius 1.5 cm, cut off QR = 1.5 cm along QX.
- Adjust the compass to a radius of 1.5 cm, place the compass point at Q, and draw an arc along ray QX. Mark the intersection point as R.

6. **Step 3**: Join points R and S to complete the quadrilateral PQRS.
- Draw a straight line connecting points R and S to complete the quadrilateral.

### Final Order of Steps:
The correct order of construction steps is: **5, 2, 4, 6, 1, 3**.