Question

Construct a quadrilateral ABCD, when AB = 6 cm, BC = 5.5 cm, CD = 4.1 cm, ∠A = 120°, ∠B = 45°

Answer 1

Given:

• AB = 6 cm
• BC = 5.5 cm
• CD = 4.1 cm
• ∠A = 120°
• ∠B = 45°

Steps of construction:

1. Draw the line segment AB = 6 cm.
2. At point A, construct an angle of 120° using a protractor.
3. At point B, construct an angle of 45° using a protractor.
4. From B, draw a ray BC making the 45° angle with AB and cut off BC = 5.5 cm on this ray.
5. Connect C.
6. Using compass and ruler, locate point D such that CD = 4.1 cm and D lies at such a position that the quadrilateral ABCD is closed.
   • To do this, draw an arc of radius 4.1 cm from C.
   • From point A, draw an arc with a suitable radius derived from construction steps to intersect the previous arc.
   • The intersection point is D.
7. Join AD and CD to complete quadrilateral ABCD.

ABCD is the quadrilateral with sides AB = 6 cm, BC = 5.5 cm, CD = 4.1 cm and angles ∠A = 120°, ∠B = 45° constructed as per the steps above.