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.