The angles of a quadrilateral ABCD are in the ratio 3:5:7:9. What type

Question

The angles of a quadrilateral ABCD are in the ratio 3:5:7:9. What type of quadrilateral is it?

A. Rectangle
B. Parallelogram 
C. Rhombus
D. Kite
E. Trapezium

GMATinsight · Answer

Ratio of angle= 3:5:7:9

Alternate angles
5+7 = 3+9

I.e. we find two pairs of complementary angles

I e. A trapezium with two sides parallel

Answer Option E

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ManishaPrepMinds · Answer

As it is a quadrilateral the sum of all the interior angles in Quadrilateral is equal to 360 degrees. 
Thus respective angles are (45 degrees, 75 degrees, 105 degrees, 135 degrees).

Properties of Parallelogram : 
Opposite angles are congruent
adjacent angles are supplementary

Property of Trapezium 
Sum of the interior angles on the same side of transversal is 180 degrees
  
Property of Kite 
One pair of diagonally opposite angles is equal in measurement

Here Opposite angles are not equal. thus we can eliminate choices A, B, C, and no two angles are equal we can eliminate choice D also.
Thus the quadrilateral is Trapezium( the sum of the interior angles on the same side of transversal is 180 degrees)
Answer: E

IanStewart · Answer

Where is the question from? It is unanswerable, and the solutions above are not correct.

You don't need to know what a "kite" is on the GMAT. You definitely don't need to know what a "trapezium" is -- mathematicians don't even agree on the definition of a "trapezium". Some use it as a synonym for "trapezoid" (a quadrilateral with a pair of parallel sides), while others use it to describe quadrilaterals with no pair of parallel sides. So there's no way to know what kind of shape answer E even describes. But the solutions above that claim the shape is a trapezoid because for adjacent angles "3 + 9 = 5 + 7" (or equivalently because adjacent angles add to 180) are not correct, because we have no way to know that's true. The question doesn't tell us in what order the angles appear around the interior of the shape. If the angles are, in clockwise order, 45, 135, 105, 75, say, then the shape is indeed a trapezoid. If instead they are, in clockwise order, 45, 105, 135, 75, then the shape is an irregular quadrilateral with no parallel sides. So regardless of which definition of "trapezium" the question is using, there's no way to be sure the shape is one, and the answer is "F", none of the above. This is not a good question and you'll never see anything remotely like it on the GMAT.

The angles of a quadrilateral ABCD are in the ratio 3:5:7:9. What type

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