in the given figure ABCDE id a pentagon inscribed in a circle. If AB=BC=CD, angle BCD= 110 and angle BAE= 120 find

(i) angle ABC

(ii) angle CDE
(iii) angle AED

(iv) angle EAD

Asked by pereiracalida | 14th Jan, 2018, 07:36: PM

Expert Answer:

begin mathsize 16px style From space the space diagram space if space you space join space BD.
In space increment BCD comma
BC equals BD space space space space space space space space space space space space space space space space space space space space space space space given
angle CBD equals angle CDB equals space straight x space space Isosceles space triangle
angle BCD equals 110 degree
angle CBD plus angle CDB plus angle BCD equals 180 degree
straight x plus straight x plus 110 degree equals 180 degree
2 straight x equals 70 degree
straight x equals 35 degree
Hence space arc space BC equals arc space CD equals arc space AB equals 2 angle CBD equals 70 degree
angle EAB equals 120 degree
arc space BCDE equals 2 cross times 120 degree equals 240 degree
arc space BC plus arc space CD plus arc space DE equals 240 degree
70 degree plus 70 degree plus arc space DE equals 240 degree
arc space DE equals 240 degree minus 140 degree
arc space DE equals 100 degree
angle BCD equals 2 cross times left parenthesis arc space DE plus arc space EA plus arc space AB right parenthesis
110 degree cross times 2 equals left parenthesis 100 degree plus arc space EA plus 70 degree right parenthesis
220 degree equals 170 degree plus space arc space EA
arc space EA equals 50 degree
angle ABC equals 1 half cross times open parentheses arc space CD plus arc space DE plus arc space EA close parentheses
angle ABC equals 1 half cross times open parentheses 70 degree plus 100 degree plus 50 degree close parentheses
angle ABC equals 110 degree
similarly space you space can space solve space for space the space remaining space angles.

end style

Answered by Sneha shidid | 16th Jan, 2018, 10:53: AM