Question

If angles P, Q, R and S of a quadrilateral PQRS taken in order are in the ratio 4:6:7:3, then
(1) Square
(2) Trapezium
(3) Parallelogram
(4) Rhombus


I want answer step by step please​

Answer 1

i think 3 one is the correct answer

Answer 2

Answer:

The ratio of angles = 4:6:7:3

Let the angles be ∠P=3x, ∠Q=7x, ∠R=6x and ∠S=4x.

In quadrilateral PQRS,

∠P+∠Q+∠R+∠S=360°

3x+7x+6x+4x=360 °

20x=360°

∴  x=18°  

⇒  ∠P=3×18=54°

⇒  ∠Q=7×18=126 °

⇒  ∠R=6×18=108°

⇒  ∠S=4×18=72°

Now,

• The quadrilateral PQRS is not a square because the angles are not 90°.

• The quadrilateral PQRS is not a parallelogram because the opposite angles are not equal.

• The quadrilateral PQRS is not a rhombus because the opposite angles are not equal.

Thus, the quadrilateral PQRS is a trapezium.

HOPE THIS HELPS :D