Question

the measure of the angle of the quadrilateral ABCD are in the ratio 2:3:4:1 determine the type of the quadrilateral​

Answer 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

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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