two sides of the quadrilateral are in the ratio of 2:3 find them
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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
o
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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