Question

ABCD is a cyclic quadrilateral BA and CD are produced to meet at E . prove that triangle EBC us equiangular to triangle EDA
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Answer 1

Answer:Construct the figure.... Name the angles as follows.a,b,c,d...according to the respective vertices ..so according to the properties of cyclic quadrilaterals a+c=180...b+d=180 ..In Triangle EBC... Angle EBC+b=180....Angle EBC =d..similarly..angle ECB+c=180...angle ECB= a....therefore in triangle EDA,ANGLE EAD=a,angle EDA=d and angle DEA is common..Hence these triangles are equiangular