In a Triangle  ABC,  where BC is produced to point D.  an interior bisector divides Angle A to meet side BC at point E . prove that Angle ABC + Angle ACD = 2 Angle AEC ....
 
 
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Asked by Poornima Sastry | 28th Jul, 2015, 05:32: PM

Expert Answer:

L e t space angle B A E equals x comma space angle E A C equals x space left square bracket because A E space i s space t h e space a n g l e space b i s e c t o r right square bracket angle A B C equals m angle A C D equals n I n space increment A E C comma angle E A C plus angle A C E plus angle A C E equals 180 degree x plus left parenthesis 180 minus n right parenthesis plus angle A C E equals 180 degree angle A C E equals n minus x  I n space increment space A B C comma angle A B C plus angle B A C equals angle A C D m plus x plus x equals n m plus 2 x equals n m plus n plus 2 x equals n plus n space left square bracket A d d i n g space angle A C D equals n space o n space b o t h space s i d e s right square bracket m plus n equals 2 n minus 2 x m plus n equals 2 left parenthesis n minus x right parenthesis S u b s t i t u t i n g space t h e space a n g l e s space w e space g e t comma angle A B C plus angle A C D equals 2 angle A C E H e n c e space P r o v e d

Answered by Prasenjit Paul | 29th Jul, 2015, 10:58: AM