Question

89. The angles P, Q, R and S of a quadrilateral are in
the ratio 1:3:7:9. Then PQRS is a​

Answer 1

Let 1:3:7:9=1x:3x:7x:9x

Sum of all angle is 360°

So,

1x+3x+7x+9x=360°

20x=360°

x=360°/20

x=18

1×18=18°

3×18=54°

7×18=126°

9×18=162°

Now consider 18+162=180°&54+126=180°

Sum of adjacent angles is 180°.Hence PQRS is a trapezium .But sum of opposite angles is not 180°.Hence PQRS is not a llgm

Answer 2

Answer:

PQRS is a parallelogram

Step-by-step explanation:

let 1:3:7:9=x:3x:7x:9x

we know that sum of angles of quadrilateral is 360°

=> x+3x+7x+9x=360°

=> 20x=360°

=> x=18°

now,

x=18°

3x=3*18=54°

7x=126°

9x=162°

as sum of opposite angles is 180° therefore it is a parallelogram