Question

ABCD is a cyclic quadrilateral whose diogonal intersect at a point E . if angle DBC=70°, angle BAC is 30°, find angle BCD. Further , if AB= AC find angle ECD​

Answer 1

Answer:

For chord CD,

∠CBD=∠CAD ...Angles in same segment

∠CAD=70°

∠BAD=∠BAC+∠CAD=30°+70°=100°

∠BCD+∠BAD=180° ...Opposite angles of a cyclic quadrilateral

⇒∠BCD+100°=180°

⇒∠BCD=80°

In △ABC

AB=BC (given)

∠BCA=∠CAB ...Angles opposite to equal sides of a triangle

∠BCA=30°

Also, ∠BCD=80°

∠BCA+∠ACD=80°

⇒30°+∠ACD=80°

∠ACD=50°

∠ECD=50°