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