Please give answer

Asked by vivekagarwal1296 | 22nd Apr, 2019, 12:41: PM

Expert Answer:

I n space t h e space g i v e n space c i r c l e comma space t h e space a n g l e space 1 space a n d space 2 space a r e space m a d e space b y space t h e space s a m e space a r c space X Y space a n d space i n space t h e space s a m e space s e g m e n t
T h e r e f o r e comma space angle 1 equals angle 2
S i m i l a r l y comma space angle 3 equals angle 4 space.... space A n g l e s space m a d e space b y space s a m e space a r c space i n space t h e space s a m e space s e g m e n t
N o w comma space A X space a n d space A Y space a r e space t h e space s t r a i g h t space l i n e s
S o comma space angle A B X space a n d space angle A C Y space a r e space s t r a i g h t space a n g l e s
T h e r e f o r e space angle A B D equals space 180 degree minus angle 2 equals 180 degree minus angle 1 space.... space S i n c e comma space angle 1 equals angle 2
A l s o comma space angle A C D equals 180 degree minus angle 1 equals angle A B D space....... space left parenthesis i right parenthesis
N o w comma space a equals angle A O Y space i s space t h e space a n g l e space m a d e space b y space a n space a r c space a t space t h e space c e n t r e space a n d space angle 1 space i s space t h e space a n g l e space m a d e space b y space t h e space s a m e space a r c space o n space t h e space c i r c l e
T h e r e f o r e comma space a equals 2 angle 1 equals 2 angle 2 space.... space left parenthesis i i right parenthesis
N o w comma space a s space angle 1 equals angle 2 space a n d space angle 3 equals angle 4
rightwards double arrow increment B D X space a n d space increment C D Y space a r e space c o n g r u e n t space a n d space h e n c e comma space angle B D X equals angle C D Y
rightwards double arrow b equals angle B D C space.... space left parenthesis i i i right parenthesis space 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
N o w comma space i n space q u a d r i l a t e r a l space A B D C
angle A B D plus angle A C D plus angle B D C plus angle B A C equals 360 degree
rightwards double arrow angle A B D plus angle A C D plus angle B D C plus c equals 360 degree
rightwards double arrow c equals 360 degree minus left parenthesis angle A B D plus angle A C D plus angle B D C right parenthesis
rightwards double arrow c equals 360 degree minus left parenthesis 180 degree minus angle 1 plus 180 degree minus angle 1 plus b right parenthesis space..... space F r o m space left parenthesis i right parenthesis space a n d space left parenthesis i i i right parenthesis
rightwards double arrow c equals 360 degree minus 360 degree plus angle 1 plus angle 1 minus b
rightwards double arrow c equals 2 angle 1 minus b
rightwards double arrow c equals a minus b space.... space F r o m space left parenthesis i i right parenthesis
H e n c e comma space c equals a minus b

Answered by Renu Varma | 23rd Apr, 2019, 10:38: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.