Find the value of a + b if a b=2 a.

Asked by sumitshekhar891 | 13th May, 2020, 02:25: PM

Expert Answer:

To find the value of a+b if b=2a in the given figure.
In the figure, ABCD is a cyclic quadrilateral.
angle B C E equals 30 degree
rightwards double arrow angle D C F equals angle B C E equals 30 degree space... space left parenthesis V e r t i c a l l y space o p p o s i t e space a n g l e s right parenthesis
angle D C B space a n d space angle B C E space f o r space a space l i n e a r space p a i r space o f space a n g l e s
rightwards double arrow angle D C B plus angle B C E equals 180 degree
rightwards double arrow angle D C B equals 150 degree
S i n c e space A B C D thin space i s space a space c y c l i c space q u a d r i l a t e r a l
rightwards double arrow angle D C B plus angle D A B equals 180 degree
rightwards double arrow angle D A B equals 30 degree
N o w space i n space triangle A B F space a n d space triangle B C E
angle F A B plus angle A B F plus b equals 180 degree space space a n d space space angle C B E plus angle B C E plus a equals 180 degree
rightwards double arrow angle F A B plus angle A B F plus b plus space angle C B E plus angle B C E plus a equals 180 degree plus 180 degree
rightwards double arrow 30 degree plus open parentheses angle A B F plus space angle C B E close parentheses plus 30 degree plus 2 a plus a equals 360 degree
rightwards double arrow 60 degree plus 180 degree plus 3 a equals 360 degree space space space space... space left parenthesis angle A B F space a n d space angle C B E space f o r space a l i n e a r space p a i r space o f space a n g l e s right parenthesis
rightwards double arrow 3 a equals 120 degree
rightwards double arrow a equals 40 degree
rightwards double arrow b equals 2 a equals 80 degree
H e n c e comma space a plus b equals 120 degree.

Answered by Renu Varma | 13th May, 2020, 04:01: PM

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