Ex 9.3, 6
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.
For segment DCBAD
∠ CBD & ∠ CAD are in the same segment
So, they must be equal
∴ ∠ CAD = ∠ CBD
∴ ∠ CAD = 70°
Also, ∠BAD = ∠BAC + ∠CAD
∠BAD = 30° + 70°
∠BAD = 100°
Now,
ABCD is a cyclic quadrilateral
∠BCD + ∠BAD = 180°
∠BCD + 100° = 180°
∠BCD = 180° – 100°
∠ BCD = 80°
Also, if AB = BC, we need to find ∠ ECD
In ∆ ABC,
AB = BC
So, ∠ BCA = ∠ BAC
∴ ∠ BCA = 30°
Also,
∠ BCD = ∠ BCA + ∠ ECD
80° = 30° + ∠ ECD
∠ ECD = 80° – 30°
∠ ECD = 50°

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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