CBSE Class 9 Answered

In the followin figure, A is the centre of the circle. ABCD isa paralleolgram and CDE is a straight line. Find BCD:ABE

Asked by kumar.ashlesha | 16 Jan, 2015, 10:24: PM

Expert Answer

A B C D space i s space a space p a r a l l e log r a m. L e t space angle C equals x comma angle A equals x angle A D C equals 180 degree minus x space left square bracket because A B C D space i s space a space p a r a l l e log r a m space a n d space angle B A D space a n d space angle A D C space a r e space c o minus i n t e r i o r space a n g l e s right square bracket angle B E C equals x over 2 left square bracket A n g l e space a t space t h e space c e n t r e space i s space h a l f space t h e space a n g l e space s u b t e n d e d space b y space t h e space a r c space a t space t h e space c i r c u m f e r e n c e right square bracket I n space increment B E C comma angle E B C equals 180 degree minus open parentheses x over 2 plus x close parentheses equals 180 degree minus fraction numerator 3 x over denominator 2 end fraction I n space parallelogram A B C D comma angle B A D plus angle A D C plus angle D C B plus angle C B A equals 360 degree rightwards double arrow x plus left parenthesis 180 degree minus x right parenthesis plus x plus angle C B A equals 360 degree rightwards double arrow angle C B A equals 360 degree minus 180 degree minus x rightwards double arrow angle C B A equals 180 degree minus x angle C B A equals angle C B E plus angle E B A rightwards double arrow 180 degree minus x equals 180 degree minus fraction numerator 3 x over denominator 2 end fraction plus angle E B A rightwards double arrow angle E B A equals 180 degree minus x minus open parentheses 180 degree minus fraction numerator 3 x over denominator 2 end fraction close parentheses rightwards double arrow angle E B A equals 180 degree minus x minus 180 degree plus fraction numerator 3 x over denominator 2 end fraction equals x over 2 therefore angle A B E equals x over 2 fraction numerator angle B C D over denominator angle A B E end fraction equals fraction numerator x over denominator begin display style x over 2 end style end fraction equals 2 over 1

Answered by Prasenjit Paul | 17 Jan, 2015, 08:53: AM

CBSE Class 9 Answered

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CBSE Class 9 Answered

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