In the given figure if ABCD is a rhombus diagonals AC and BD intersect at o   and he is a point lying on the circle with Centre o then the sum of the measures of angle BAE and angle EDC is?? 

Asked by shriya.pandey182 | 20th Oct, 2017, 11:01: PM

Expert Answer:

begin mathsize 12px style m angle B O C equals 90 degree space space space space left parenthesis D i a g o n a l s space o f space a space r h o m b u s space a r e space p e r p e n d i c u l a r right parenthesis

m left parenthesis a r c space B E C right parenthesis equals m angle B O C space space space left parenthesis M e a s u r e space o f space t h e space c e n t r a l space a n g l e space i s space e q u a l space t o
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space t h e space m e a s u r e space i f space t h e space i n t e r c e p t e d space a r c right parenthesis

therefore m left parenthesis a r c space B E C right parenthesis equals 90 degree space....... space left parenthesis 1 right parenthesis

m angle B A E equals 1 half m left parenthesis a r c space B E right parenthesis space.. left parenthesis 2 right parenthesis
m angle E D C equals 1 half m left parenthesis a r c space E C right parenthesis space space... left parenthesis 3 right parenthesis space space left parenthesis M e a s u r e space o f space t h e space i n s c r i b e d space a n g l e space i s space h a l f space t h e space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space m e a s u r e space o f space t h e space i n t e r c e p t e d space a r c right parenthesis


A d d i n g space e q u a t i o n s space 2 space a n d space 3 comma
m angle B A E plus m angle E D C equals 1 half m left parenthesis a r c space B E right parenthesis plus 1 half m left parenthesis a r c space E C right parenthesis
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half left square bracket m left parenthesis a r c space B E right parenthesis plus m left parenthesis a r c space E C right parenthesis right square bracket
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half m left parenthesis a r c space B E C right parenthesis space space space space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half cross times 90 degree space..... space left parenthesis f r o m space 1 right parenthesis
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 45 degree

therefore m angle B A E plus m angle E D C equals 45 degree

space space space space space space space space space space space space space
end style

Answered by Nooren | 15th Dec, 2017, 11:02: AM