In a circle with centre O, a diameter AB and a chord CD intersect each other at E, AC and AD are joined. If $$\angle$$BOC= $$48^\circ$$ and $$\angle$$AOD = $$100^\circ$$, then what is the measure of $$\angle$$CEB ?

Angle BOC= 48 so, Angle BAC = 24  (The angle subtended at the centre is twice to that of angle subtended at the circumference by the same arc)

Angle AOD = 100 so, Angle ACE = 50 (The angle subtended at the centre is twice to that of angle subtended at the circumference by the same arc)

In triangle ACE,

Angle AEC = 180- (50+24) = 106

So, angle CEB = 180 - 106 = 74 degrees (Straight line is 180 degrees).