Question

In the given figure , if aob is a diameter of a circle , with centre o angle ebd =15 degrees and acd=120 degrees.Find the measure of abe.

Answer 1

Step-by-step explanation:

Given- 

O is the centre of a circle of which AOB is a diameter.

CD is another chord, intersecting AOBˉ.

∠BOD=120o

To find out- ∠ACD=? 

Solution-

∠AOD=180o−∠BOD=180o−120o=60o ....(linear pair).

Now ∠AOD is the angle subtended by the minor arcAD to the centre and ∠ACD is the angle subtended by the minor arc AD to the circumference at C.

∴∠ACD=21∠ACD=21×60o=30