1. If an isosceles triangle ,a base is four times its vertices angle. Find all the angles of the triangle

Asked by Isra | 12th Dec, 2015, 04:07: PM

Expert Answer:

L e t space triangle A B C space b e space a n space i s o s c e l e s space t r i a n g l e comma space w i t h space v e r t e x space A. T h u s comma space angle B A C space i s space i t s space v e r t e x space a n g l e space a n d space angle A B C space a n d space angle C B A space a r e space i t s space b a s e space a n g l e s. I n space a n space i s o s c e l e s space t r i a n g l e comma space t h e space b a s e space a n g l e s space a r e space e q u a l. rightwards double arrow angle A B C equals angle C B A... left parenthesis 1 right parenthesis G i v e n space b a s e space a n g l e space i s space f o u r space t i m e s space t h e space v e r t e x space a n g l e. rightwards double arrow angle A B C equals angle C B A equals 4 angle B A C... left parenthesis 2 right parenthesis B y space a n g l e space s u m space p r o p e r t y comma space w e space h a v e angle B A C plus angle A B C plus angle C B A equals 180 degree rightwards double arrow angle B A C plus angle C B A plus angle C B A equals 180 degree space space space space space space open square brackets u sin g space e q u a t i o n space left parenthesis 1 right parenthesis close square brackets rightwards double arrow angle B A C plus 2 angle C B A equals 180 degree rightwards double arrow angle B A C plus 2 open parentheses 4 angle B A C close parentheses equals 180 degree space space space space space space space space space space space space space open square brackets u s i n g space e q u a t i o n space left parenthesis 2 right parenthesis close square brackets rightwards double arrow angle B A C plus 8 angle B A C equals 180 degree rightwards double arrow 9 angle B A C equals 180 degree rightwards double arrow angle B A C equals fraction numerator 180 degree over denominator 2 end fraction rightwards double arrow angle B A C equals 20 degree rightwards double arrow angle A B C equals angle C B A equals 4 angle B A C equals 4 cross times 20 degree equals 80 degree T h u s space t h e space a n g l e s space o f space t h e space t r i a n g l e space i s space 20 degree comma space 80 degree comma space 80 degree

Answered by Vimala Ramamurthy | 13th Dec, 2015, 11:49: AM

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