In the given figure, chord ED is parallel to diameter AC of the circle. Given ∠CBE = 65o, calculate ∠DEC.

Solution:

Join

   

   

subtends

   

at the centre and

   

at the remaining part of the circle.

   

Now, in

   

   

[Radii of the same circle]

So,

   

But, in

   

by angle sum property

   

 [Angles of a triangle]

   

Or,

   

   

So,

   

And,

   

[Given]

   

[Alternate angles]

Thus,