Question

the angles p,q,r,s of a quadrilateral are in the ratio 1:3:7:9
i]find the measure of each angle
ii]is p,q,r,s a trapezium?why?
iii]is p,q,r,s a parallelogram?why?

Answer 1

Suppose the angles are x,3x, 7x & 9x. Sum of all angles of a quadrilateral is 360. Hence x + 3x + 7x + 9x = 360. 20x = 360. X = 18. angles are 18, 54, 126, 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 it is not a parallelogram.

Answer 2

Answer:

Each angle of quadrilateral is 18° ,54°,126° ,162° and PQRS is a trapezium not a parallelogram.

Step-by-step explanation:

Ratio of angles are 1 :3 :7 :9

Let angles are x, 3x, 7x, 9x

Sum of all the angles of a quadrilateral = 360°

So, x + 3x+ 7x + 9x =360°

              20x =360°

               x = 360 /20 = 18°

Other angles are , 3 × 18 =54°

                              7 × 18 =126°

                              9 × 18 =162°

As we know that,

Sum of Adjacent angles of a parallelogram and trapezium are  180°

But opposite angle of parallelogram are same but trapezium has different.

In quadrilateral PQRS we see that 54° + 126° =180°

But other two angles 18° and 162° are not same

So, PQRS is a trapezium not a parallelogram.