Question

Measures of angles of □A?ABCD are in the ratio 4 ∶ 5 ∶ 7 ∶ 8. Show that □A?ABCD is a

trapezium.​

Answer 1

Answer:

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Answer 2

Answer:

Let the angles of the quadrilateral in degrees be =2a,3a,4a and a

Since the sum of angles of a quadrilateral =360

o

,

2a+3a+4a+a=360

10a=360 o

a=36

So,

the angles of the quadrilateral are =2a=72 o

,3a=108 o

,4a=144

o and a=36

Suppose ∠A=72 o

and ∠B=108 o

Sum of ∠A and ∠B=72 o

+108 o

=180 o

This means, AB is a transversal to the parallel sides AD and BC as the sum of

interior angles on the same side of transversal is 180

o

Hence, AD∥BC and ABCD is a trapezium.