Quadrilateral ABCD Which have PQ= 5cm QR=6.5cm angle p= angle R = 100degree and angleS=75degree so make construction of quadrilateral 

To construct a quadrilateral \(ABCD\) with given sides and angles, we'll follow a systematic approach to create a precise drawing. However, it appears there is some ambiguity in the way the quadrilateral's sides and angles are described in your question. Let’s assume you meant:

- \(PQ = 5 \, \text{cm}\)
- \(QR = 6.5 \, \text{cm}\)
- \(\angle P = 100^\circ\)
- \(\angle R = 100^\circ\)
- \(\angle S = 75^\circ\)

We'll assume \(P\), \(Q\), \(R\), and \(S\) refer to points on the quadrilateral \(ABCD\). For this construction, let’s proceed step-by-step:

### Step-by-step Construction of the Quadrilateral

1. **Draw Base \(PQ\):**
   - Draw a line segment \(PQ = 5 \, \text{cm}\).

2. **Construct Angle \(\angle P = 100^\circ\):**
   - At point \(P\), use a protractor to measure and draw an angle of \(100^\circ\). 

3. **Draw Side \(QR\):**
   - From point \(P\), draw line \(PR\) such that \(PR = 6.5 \, \text{cm}\) at the measured angle.

4. **Construct Angle \(\angle R = 100^\circ\):**
   - At point \(R\), use a protractor to measure an angle of \(100^\circ\). 

5. **Locate Point \(S\) Using \(\angle S = 75^\circ\):**
   - From point \(Q\), draw a line at \(75^\circ\) until it meets the line from step 4. Label the intersection point as \(S\).

6. **Draw Remaining Sides:**
   - Connect \(S\) to \(P\) and \(Q\) to complete the quadrilateral.

### Conclusion

- You now have a quadrilateral \(PQRS\) with the specified side lengths and angles.

Would you like any further details, or do you have questions about these steps?

### Follow-up Questions:

1. Would you like to understand how to measure and draw angles using a protractor?
2. Are there any other types of quadrilaterals you want to learn to construct?
3. Do you need guidance on understanding properties of different quadrilaterals?
4. Would you like to explore the internal angle sum properties of quadrilaterals?
5. Are you interested in learning how to calculate the area of a quadrilateral given side lengths and angles?

**Tip:** Always ensure your compass and protractor are accurate to maintain the precision of your constructions.

Learn how to construct quadrilateral ABCD with sides PQ = 5cm, QR = 6.5cm and angles ∠P = ∠R = 100°, ∠S = 75°. Follow this step-by-step guide to create a precise drawing using geometric principles and angle measurements. Suitable for students in Grades 6-8.

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