In the given figure, O is the centre of circle. If ED||AC and angle EBC = 60, find the measure of angle DEC.

Soln:

i. Angle EAC = Angle EBC = 60 [Inscribed angle standing on the same arc EC]
ii. Angle AEC = 90 [An angle at the semi circle]
iii. In triangle angle ACE = 180-90-60=30 [Sum of angles of a triangle]
iv. Angle ACE = Angle DEC=30 [Being alternate angles]