Question

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ZDBC =70°,
ZBAC is 30°, find Z BCD. Further, if AB = BC, find ZECD.​

Answer 1

Answer:

this is diagram ☝️☝️☝️☝️☝️

Step-by-step explanation:

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°