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

trapezium.​

2 thoughts on “Measures of angles of □A?ABCD are in the ratio 4 ∶ 5 ∶ 7 ∶ 8. Show that □A?ABCD is a <br /><br />trapezium.​”

1. Answer:

   idk bruh I’m just doing this because I have to

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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.

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