QUESTION) ONE OF THE DIAGNOLS OF A RHOMBUS IS EQUAL TO ONE OF ITS SIDES.FIND THE ANGLES OF THE RHOMBUS

Asked by vrishti TOKAS | 21st May, 2014, 06:40: PM

Expert Answer:

G i v e n space t h a t space o n e space o f space t h e space d i a g o n a l s space o f space a space r h o m b u s space i s space e q u a l space t o space t h e space s i d e space o f space t h e space r h o m b u s. L e t space apostrophe a apostrophe space b e space t h e space s i d e space o f space t h e space r h o m b u s. S i n c e space t h e space d i a g o n a l s space b i s e c t space e a c h space o t h e r space a t space r i g h t space a n g l e s comma space i t space f o r m s space r i g h t space t r i a n g l e space w i t h space b a s e comma space apostrophe a over 2 apostrophe space a n d space h y p o t e n u s e space apostrophe a apostrophe O b s e r v e 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 theta equals angle O D A sin theta equals fraction numerator O A over denominator A D end fraction equals fraction numerator begin display style a over 2 end style over denominator a end fraction equals 1 half rightwards double arrow theta equals 30 degree rightwards double arrow angle D A O equals 60 degree S i n c e space t h e space s i d e s space A B space a n d space C D space a r e space p a r a l l e l space t o space e a c h space o t h e r comma space w e space h a v e angle O B C equals 30 degree space a n d space angle O C B equals 60 degree S i m i l a r l y comma space sin angle O D C equals fraction numerator O A over denominator A D end fraction equals fraction numerator begin display style a over 2 end style over denominator a end fraction equals 1 half rightwards double arrow angle O D C equals 30 degree N o w space c o n s i d e r space t h e space a n g l e space angle A D C equals angle O D A plus angle O D C equals 60 degree S i n c e space t h e space o p p o s i t e space a n g l e s space o f space a space r h o m b u s space a r e space e q u a l comma space w e space h a v e comma angle A B C equals 60 degree A n d space t h e space a d j a c e n t space a n g l e s space o f space t h e space r h o m b u s space a r e space s u p p l e m e n t a r y comma space w e space h a v e comma angle B A D equals 120 degree. T h u s comma space t h e space a n g l e s space o f space t h e space r h o m b u s space a r e space 60 degree comma space 120 degree comma space space 60 degree space a n d space 120 degree

Answered by Vimala Ramamurthy | 22nd May, 2014, 09:58: AM

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