Question

in a quadrilateral pqrs the angle are in the ratio 3:4:5:6find the angle of quadrilateral find the angle of pqrs what is the special name given to pqrs​

Answer 1

Answer:

The angles are 60° , 80° , 100°, 120°

The special name is Trapezium

Step-by-step explanation:

Let-

∠1 = 3x

∠2 = 4x

∠3 = 5x

∠4 = 6x

As we all know SUM of all 4 SIDES of a Quadrilateral = 360

⇒ ∠1 + ∠2 + ∠3 + ∠4 = 360

⇒ 3x + 4x + 5x + 6x = 360

⇒ 18x = 360

⇒ x = 360/ 18

             = 20

Therefore the angles are :

P = ∠1 = 3*20 = 60°

Q = ∠2 = 4*20 = 80°

R = ∠3 = 5*20 = 100°

S = ∠4 = 6*20 = 120°

Here the opposite angles are ∠1 and ∠4 , ∠2 and ∠3  

P + S = ∠1 + ∠4 = 60° + 120° = 180°

Q + R = ∠2 + ∠3 = 80° +100° = 180°

⇒ PS || QR and PS = QR

Since one pair of opposite sides are equal and parallel the special name given is TRAPEZIUM

hope it helps you..