Question

Chord AB and DC where produced intersect at E. Show that triangle AED and triangle CEB are equiangular.

Answer 1

m∠ADC = m∠CBE  --------->  Exterior angle = Remote opposite interior angle of cyclic quadrilateral

m∠DAB = m∠BCE  --------->  Exterior angle = Remote opposite interior angle of cyclic quadrilateral

m∠BEC = m∠CEB  ----------> Self congruence

∴ ΔBCE is similar to ΔADE

Hence the 2 triangles are equiangular.

Hope this helps! :)