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Question

The angles of a quadrilateral are in the ratio 3: 4: 5: 6. Then the quadrilateral is a trapezium.

A
True
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B
False
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Solution

The correct option is A True
LetA,B,Cand DbetheanglesofquadilateralA=3x,B=4x,C=5xandD=6x,wherexisaconstant inquadilateralABCDA+B+C+D=360o (Anglesumproperty)3x+4x+5x+6x=36018x=360ox=20oA=3x=3×20=60oB=4x=4×20=80oC=5x=5×20=100oD=6x=6×20=120o
InquadilateralABCDA+D=60+120=180oB+C=80+100=180oABCD(Sumofconsecutiveinteriorangleissupplementary)ButA+B=60+80180oADisnotparalleltoBCHencequadilateralisatrapzium(asithasonlyonepairofparallelside)\\

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