prove that the sum of angles of a triangle is 180.Using this find all the angles of a triangle if the angles are in the ratio 1:2:3.
Give your view how the measure of angles useful in making furniture?
Is accuracy necessary in measurements?

Asked by kumarasia | 22nd Sep, 2014, 08:47: AM

Expert Answer:

C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
 
L e t space A B C space b e space a space t r i a n g l e. C o n s t r u c t i o n : D r a w space a space l i n e space P A Q space p a r a l l e l space t o space B C S i n c e space B C space i s space p a r a l l e l space t o space P Q comma space a n d space A B space i s space a space t r a n s v e r s a l comma space w e space h a v e comma angle P A B equals angle A B C... left parenthesis 1 right parenthesis S i n c e space B C space i s space p a r a l l e l space t o space P Q comma space a n d space B C space i s space a space t r a n s v e r s a l comma space w e space h a v e comma angle C A Q equals angle A C B... left parenthesis 2 right parenthesis S i n c e space P A Q space i s space a space s t r a i g h t space l i n e comma space w e space h a v e comma angle P A Q space i s space a space s t r a i g h t space a n g l e. rightwards double arrow angle P A Q equals angle P A B plus angle B A C plus angle C A Q equals 180 degree.... left parenthesis 3 right parenthesis S u b s t i t u t i n g space t h e space v a l u e s space o f space angle P A B space a n d space angle C A Q space f r o m space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis space i n space e q u a t i o n space left parenthesis 3 right parenthesis comma space w e space h a v e comma angle A B C plus angle B A C plus angle A C B equals 180 degree. H e n c e space t h e space a n g l e space s u m space p r o p e r t y space i s space p r o v e d.
G i v e n space t h a t space t h e space a n g l e s space o f space a space t r i a n g l e space a r e space i n space t h e space r a t i o space 1 : 2 : 3 T h a t space i s space t h e space a n g l e s space a r e space x comma space 2 x space a n d space 3 x. B y space a n g l e space s u m space p r o p e r t y comma space x plus 2 x plus 3 x equals 180 degree rightwards double arrow 6 x equals 180 degree rightwards double arrow x equals fraction numerator 180 degree over denominator 6 end fraction rightwards double arrow x equals 30 degree T h u s space t h e space a n g l e s space a r e space 30 degree comma 60 degree space a n d space 90 degree
 
 

Answered by Vimala Ramamurthy | 22nd Sep, 2014, 10:49: AM