Construct a quadrilateral ABCD, in which AB = 5.9cm , angle ABC = 70 deg BC = 4.9cr angle BCD = 120 deg and angle CDA = 40 deg .


To construct the quadrilateral ABCD with the given measurements and angles, you can follow these steps:

### Given:
- \( AB = 5.9 \, \text{cm} \)
- \( \angle ABC = 70^\circ \)
- \( BC = 4.9 \, \text{cm} \)
- \( \angle BCD = 120^\circ \)
- \( \angle CDA = 40^\circ \)

### Step-by-Step Construction:

1. **Draw Line Segment AB:**
   - Use a ruler to draw a line segment \( AB \) of length 5.9 cm.

2. **Construct Angle ABC:**
   - At point \( B \), use a protractor to construct an angle of \( 70^\circ \) with \( AB \). This is \( \angle ABC \).

3. **Draw Line Segment BC:**
   - Along the line formed by \( \angle ABC \), measure a distance of 4.9 cm from point \( B \). Mark this point as \( C \). Now, \( BC = 4.9 \, \text{cm} \).

4. **Construct Angle BCD:**
   - At point \( C \), use a protractor to construct an angle of \( 120^\circ \). This is \( \angle BCD \).

5. **Draw Line Segment CD:**
   - Extend the line formed by \( \angle BCD \). We do not know the exact length of \( CD \) yet.

6. **Construct Angle CDA:**
   - Now, at point \( D \), use a protractor to measure an angle of \( 40^\circ \). This is \( \angle CDA \). Extend the line such that it intersects with the extension of line \( AD \).

7. **Find Point D:**
   - The intersection of the lines drawn from steps 5 and 6 determines point \( D \).

8. **Complete Quadrilateral ABCD:**
   - Connect points \( A \) and \( D \) to complete the quadrilateral \( ABCD \).

### Final Check:

- Verify that the angles \( \angle ABC = 70^\circ \), \( \angle BCD = 120^\circ \), and \( \angle CDA = 40^\circ \) are correct.
- Make sure that the sides \( AB = 5.9 \, \text{cm} \) and \( BC = 4.9 \, \text{cm} \) are as specified.

Would you like more details on any of the steps, or have any questions?

### Related Questions:
1. How do you use a compass and protractor in geometric constructions?
2. How to verify the constructed quadrilateral is accurate?
3. What are the properties of a general quadrilateral?
4. How to calculate the area of a quadrilateral given its sides and angles?
5. What types of quadrilaterals are there, and how do they differ?

**Tip:** Always double-check your measurements and angles to ensure accuracy in constructions.

Construct a quadrilateral ABCD, in which AB = 5.9cm, angle ABC = 70 degrees, BC = 4.9cm, angle BCD = 120 degrees, and angle CDA = 40 degrees.

Learn how to construct quadrilateral ABCD with sides AB = 5.9 cm, BC = 4.9 cm, and angles ABC = 70°, BCD = 120°, CDA = 40°. This step-by-step guide is perfect for middle school students studying geometric constructions and angle measurements.

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