In Fig. ABCD is a cyclic quadrilateral in which AC and BD are its d

1.	In Fig. ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC = 55° and ∠BAC = 45°, find ∠BCD.
Answer» Since angles on the same segment of a circle are equal Therefore, ∠CAD = ∠DBC = 55° ∠DAB = ∠CAD + ∠BAC = 55° + 45° = 100° But, ∠DAB + ∠BCD = 180° (Opposite angles of a cyclic quadrilateral) Therefore, ∠BCD = 180° – 100° ∠BCD = 80°

In Fig. ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC = 55° and ∠BAC = 45°, find ∠BCD.

Answer»

Since angles on the same segment of a circle are equal

Therefore,

∠CAD = ∠DBC = 55°

∠DAB = ∠CAD + ∠BAC

= 55° + 45° = 100°

But,

∠DAB + ∠BCD = 180°

(Opposite angles of a cyclic quadrilateral)

Therefore,

∠BCD = 180° – 100°

∠BCD = 80°

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In Fig. ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC = 55° and ∠BAC = 45°, find ∠BCD.

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