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ICSE Class 9 Answered

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 | 14 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 | 16 Jan, 2018, 10:53: AM

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