. The angles A, B, C and D of a quadrilateral ABCDare in the ratio 2:4 – InterviewSolution

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1.	. The angles A, B, C and D of a quadrilateral ABCDare in the ratio 2:4 5:7. Find the measures ofthese angles. What type of quadrilateral is it ?Give reasons.[Board Term II, 2012, Set 15]
Answer» Let the ratio be x so angles of ABCD are2x, 4x, 5x and 7x.sum of angles in a quadrilateral is 360°.2x + 4x + 5x + 7x = 360°18x = 360°x = 20oSo, the angles are A = 40°, B = 80°, C = 100°and D = 140°A + D = 40°+ 140°= 180°B + C = 80°+ 100° = 180°So, ABCD is a trapezium with AB parallel to CD.

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