You visited us 1 times! Enjoying our articles? Unlock Full Access!

Construction of a Quadrilateral When Two Adjacent Sides and Three Angles Are Given

Construct a q...

Question

Construct a quadrilateral ABCD, where AB = 3.5 cm, BC = 3 cm, CD = 4 cm and $∠ C = 120^{\circ}$ and $∠ B = 75^{\circ}$ . [4 MARKS]

Open in App

Solution

Steps of constructions : 1 Mark
Construction : 3 Marks

Steps of Construction:

1. Draw a line segment BC = 3cm.
2. At C construct a $120^{\circ}$ angle and draw a ray.
3. With C as centre draw an arc at the length of 4 cm. Let this line segment be CD. ie, CD = 4 cm.
4. At B construct a $75^{\circ}$ angle and draw a ray.
5. With B as centre draw an arc at the length of 3.5 cm. Let this line segment be BA. ie, BA = 3.5 cm.
6. Join AD to complete quadrilateral ABCD.

Suggest Corrections

Similar questions

Construct a quadrilateral ABCD given that AB = 4 cm, BC = 3 cm, $∠ A = 75^{\circ}, ∠ B = 80^{\circ}$ and $∠ C = 120^{\circ}$ .

Given below are the steps for the construction of a quadrilateral ABCD, where AB = 3.5 cm, BC = 6.5 cm, $∠ A = 75^{\circ}, ∠ B = 105^{\circ}$ and $∠ C = 120^{\circ}$ . Which of the following is wrong?
1:- Draw AB = 3.5 cm.
2:- Construct $∠ D A B = 75^{\circ}, ∠ A B C = 105^{\circ}$ at B.
3:- Draw BC = 6.5 cm.
4:- At D construct $∠ A D C = 120^{\circ}$ .

Q. Construct a quadrilateral

A B C D

, where

A B = 4 c m, B C = 5 c m, C D = 6.5 c m

and angle

B = 75^{o}

and angle

C = 60^{o}

Join BYJU'S Learning Program

Construct a quadrilateral ABCD, where AB = 3.5 cm, BC = 3 cm, CD = 4 cm and ∠C=120∘ and ∠B=75∘. [4 MARKS]

Construct a quadrilateral ABCD, where AB = 3.5 cm, BC = 3 cm, CD = 4 cm and $∠ C = 120^{\circ}$ and $∠ B = 75^{\circ}$ . [4 MARKS]