Question

In PQRS, angle P = x+10, angle Q = 2x+20, angle R = 3x-30 and angle S = 2x-40. Prove that

PQRS is a trapezium.​

Answer 1

-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413-14,321,413

Answer 2

Answer:

Sum of all angle of quadrilateral is 360

x+10+2x+20+3x-30+2x-40=360

8x-40=360

8x=400

x=50

Now,angle P=50+10=60

angle Q=2(50)+20=120

angle R=3(50)-30=120

angle R=2(50)-40=60

Now,angle Q + angle R=180

but these are co-interior angle

So,PQ||RS

Hence,PQRS is a trapezium.