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

trapezium.​

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:

    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.

Leave a Comment