Question

The angles of quadrilateral are 3:4:5:6.Show that quadrilateral is a trapezium

Answer 1

Let all the angles of the quardrilateral be 3x, 4x, 5x and 6x
We know that,
sum of all the angles of quardrilateral= 360
3x+4x+5x+6x= 360
18x= 360
x= 20
now the angles will be,
60, 80, 100 and 120


Clearly here,
60+120= 80+100


Since, the sum of the interior angles is 180, there exists one pair of parallel side.
Therefore, the quardrilateral is a trapezium.

HENCE PROVED.




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