Find the measure of each angle of a parallelogram if one of its angles is 30 degrees less than twice the smaller angle.



Asked by avantikadandapani | 17th Nov, 2014, 07:05: PM

Expert Answer:

I n space a space p a r a l l e log r a m space o p p o s i t e space a n g l e s space a r e space e q u a l space a n d space t h e space a d j a c e n t space a n g l e s space a r e space s u p p l e m e n t a r y. L e t space x space a n d space y space a r e 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 p a r a l l e log r a m space a n d space l e t space x greater than y G i v e n space t h a t space o n e space o f space i t s space a n g l e s space i s space 30 space d e g r e e s space l e s s space t h a n space t w i c e space t h e space s m a l l e r space a n g l e. T h a t space i s comma space x equals 2 y minus 30 degree S i n c e comma space x plus y equals 180 degree comma space w e space h a v e comma 2 y minus 30 degree plus y equals 180 degree rightwards double arrow 3 y minus 30 degree equals 180 degree rightwards double arrow 3 y equals 180 degree plus 30 degree rightwards double arrow 3 y equals 210 degree rightwards double arrow y equals fraction numerator 210 degree over denominator 3 end fraction rightwards double arrow y equals 70 degree S u b s t i t u t i n g space t h e space v a l u e space o f space y space i n space space x plus y equals 180 degree ; T h u s comma space w e space h a v e comma space x plus 70 degree equals 180 degree rightwards double arrow space x equals 180 degree minus 70 degree rightwards double arrow space x equals 110 degree T h u s space t h e space a n g l e s space o f space t h e space p a r a l l e log r a m space a r e : space 110 degree comma space 70 degree comma space 110 degree comma space 70 degree

Answered by Vimala Ramamurthy | 18th Nov, 2014, 08:36: AM