Question

construct a quadrilateral pqrs in which angle P is equal to angle are equal to 60 degree and angle Q equal to 120 degree and Angle PQ and QR equal to 4 cm.​

Answer 1

Step-by-step explanation:

Construct a quadrilateral ABCD, where sides adjacent sides AB & BC = 5 cm & 3 cm respectively. Also three angles the vertices A, B & C are 120 degree, 110 degree and 90 degree respectively. 

Solution: As per given question: 

AB = 5 cm 

BC = 3 cm 

Angle A = 120 degree 

Angle B = 110 degree 

Angle C = 90 degree 

Step of construction are as follows: 

Step 1: Draw as line segment AB of 5 cm (as shown below) 

 Construct a quadrilateral ABCD, where sides adjacent sides AB & BC = 5 cm & 3 cm respectively. Also three angles the vertices A, B & C are 120 degree, 110 degree and 90 degree respectively. 

Solution: As per given question: 

AB = 5 cm 

BC = 3 cm 

Angle A = 120 degree 

Angle B = 110 degree 

Angle C = 90 degree 

Step of construction are as follows: 

Step 1: Draw as line segment AB of 5 cm (as shown below) 

 

Step 2: Use protractor and draw angle of 120 degree at vertex A (as shown below): 

( you can also draw 120 degree angle with the help of compass. To study how to construct 120 degree angle with the help of compass Click here ) 

 

Step 3: Use protractor and draw angle of 110 degree at vertex B (as shown below): 

 

Step 4: Use compass and 3 cm wide open. With B as center, draw an arc with cuts the arm of 110 degree angle; drawn in step 3. And mark point of intersection as C (as shown below) 

 

Step 5: Use protractor and draw angle of 90 degree at point C (as shown below): 

( you can also draw 90 degree angle with the help of compass. To study how to construct 90 degree angle with the help of compass Click here ) 

 

Step 6: You can observe that arm of 90 degree angle cuts the arm of angle 120 degree angle. Mark point of this intersection as D. And we get resultant Quadrilateral ABCD (as shown below): 



Step 2: Use protractor and draw angle of 120 degree at vertex A (as shown below): 

( you can also draw 120 degree angle with the help of compass. To study how to construct 120 degree angle with the help of compass Click here ) 

 

Step 3: Use protractor and draw angle of 110 degree at vertex B (as shown below): 

 

Step 4: Use compass and 3 cm wide open. With B as center, draw an arc with cuts the arm of 110 degree angle; drawn in step 3. And mark point of intersection as C (as shown below) 

 

Step 5: Use protractor and draw angle of 90 degree at point C (as shown below): 

( you can also draw 90 degree angle with the help of compass. To study how to construct 90 degree angle with the help of compass Click here ) 

 

Step 6: You can observe that arm of 90 degree angle cuts the arm of angle 120 degree angle. Mark point of this intersection as D. And we get resultant Quadrilateral ABCD (as shown below): 



Answer 2

$pqrs$ is the required quadrilateral.

Step-by-step explanation:

Given,

Construct a quadrilateral $pqrs$,

$\angle p=\angle r=60\ degree$,$\angle q=120\ degree$ and $pq=qr=4\ cm$

Following steps:

• Draw a line segments $pq=4\ cm$ using scale.
• Draw angle $60\ degree\ and\ 120\ degree$ at $p\ and\ q$ like $\angle qpx=60\ degree\ and\ \angle\ pqy=120\ degree$
• Cuts a point $r$ on line $qy$ like $qr=4\ cm$
• At $r$, draw an angle $60\ degree$ like $\angle qrs=60\ degree$

Now, $pqrs$ is the required quadrilateral.