Question

ABCD is a cyclic quadrilatreal whose diagonals intersect at a point E . If ∠DBC = 70° , ∠BAC is 30° , find ∠BCD . Further , if AB=BC , find ∠ECD .

Answer 1

Step-by-step explanation:

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°