Question

ABCD is a cyclic quad with O as the centre of the circle. If angle BOD =136°, find angle BCD

Answer 1

∠BOD = 160 0 ( given and it’s a central angle )

∴ ∠BAD = ½ ∠BOD = 80 0 

As ABCD is a cyclic-quadrilateral, 

⇒ ∠BAD + ∠BPD = 180 

80 + ∠BPD = 180

⇒ ∠BPD = 100 

⇒ ∠BCD = 100  ( Angles in the same segment )

Answer 2

Answer: ∠BOD = 160 0 ( given and it’s a central angle )

∴ ∠BAD = ½ ∠BOD = 80 0 

As ABCD is a cyclic-quadrilateral, 

⇒ ∠BAD + ∠BPD = 180 

80 + ∠BPD = 180

⇒ ∠BPD = 100 

⇒ ∠BCD = 100  ( Angles in the same segments)

Step-by-step explanation: