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CBSE Class 9 Answered

A, B, C, D are four points on a circle. AC and BD intersect at E such that BEC=140 and angle ECD=25, then find the measure of angle BAC.
Asked by Jerlin George | 04 Jan, 2015, 03:25: PM
answered-by-expert Expert Answer
C o n s i d e r space t h e space a b o v e space f i g u r e. J o i n space A B comma space B C space a n d space A D. G i v e n space t h a t space angle B E C equals 140 degree A n d space A E C space i s space a space s t r a i g h t space l i n e. T h u s space angle B E C space a n d space angle A E B space a r e space s u p p l e m e n t a r y space a n g l e s rightwards double arrow angle B E C plus angle A E B equals 180 degree rightwards double arrow 140 degree plus angle A E B equals 180 degree rightwards double arrow angle A E B equals 180 degree minus 140 degree rightwards double arrow angle A E B equals 40 degree W e space k n o w space t h a t space t h e space a n g l e s space i n space t h e space s a m e space s e g m e n t space a r e space e q u a l. T h u s comma space angle E C D equals angle A C D equals angle A B D rightwards double arrow angle A C D equals angle A B D equals 25 degree space space space space space open square brackets g i v e n close square brackets rightwards double arrow angle A B E equals 25 degree space N o w space c o n s i d e r space t h e space t r i a n g l e space A B E B y space a n g l e space s u m space p r o p e r t y space w e space h a v e comma angle A E B plus angle A B E plus angle B A E equals 180 degree rightwards double arrow 40 degree plus 25 degree plus angle B A E equals 180 degree rightwards double arrow 65 degree plus angle B A E equals 180 degree rightwards double arrow angle B A E equals 180 degree minus 65 degree rightwards double arrow angle B A E equals 115 degree rightwards double arrow angle B A C equals 115 degree
Answered by Vimala Ramamurthy | 04 Jan, 2015, 05:04: PM

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CBSE 9 - Maths
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CBSE 9 - Maths
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