Question

ABCD is a cyclic quadrilateral whose diagonals are intersect at a point E. If
∠DBC=70° ∠BAC is 40°, find ∠BCD. Further if AB=BC, find ∠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°

Step-by-step explanation:

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Answer 2

Answer:

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