Question

In the adjoining figure. AB is the diameter
of
the circle
E is not the centre
find angle x
angle ACD = 30° "​

Answer 1

Answer:

Since AB is diameter,

∠AEB=90  

∘

 ...[Angle formed in a semi circle].

In △AEB

∠ABE=180−∠EAB−∠AEB ...[Angle sum property]

∠ABE=180–65−90=25  

∘

.

Given, ED∥AB.

⟹∠DEB=∠EBA=25  

∘

 ...[Alternate interior angles].

Since EDCB is a cyclic quadrilateral opposite angles are supplementary

Then, ∠DEB+∠DCB=180  

∘

 

⟹∠DCB=180–25=155  

∘