Question

ABCD is a cyclic quadrilateral in which AC and BD are its Diagonals. If angle DBC is 55degrees and angle BAC is 45degrees find angle BCD.

Answer 1

given that ∠CAD = ∠DBC = 55     (Since angles in the same segment)

∠DAB = ∠CAD + ∠BAC

         = 55 + 45

         = 100

similarly ∠DAB + ∠BCD = 180   (Opposite angle of a cyclic quadilateral)

 => ∠BCD = 180 - ∠DAB

                = 180 - 100

=> ∠BCD = 80

Answer 2

Given:

• ABCD is a cyclic quadrilateral
• AC and BD are its diagonals
• ∠DBC = 55° and ∠BAC = 45°

To Find:

• ∠BCD

Solution:

• The angle in the figure of the same arc are equal.
• Therefore, ∠DBC = ∠DAC
• ⇒∠DAC = 55°
• Now, ∠DAB = ∠DAC + ∠CAB
• ⇒∠DAB = 55° + 45° = 100°
• ⇒∠DAB = 100°
• We know that the sum of opposite angles of a cyclic quadrilateral is always equal to 180°
• ∴ ∠BCD + ∠DAB = 180°
• ⇒ ∠BCD = 180° - ∠DAB
• ⇒ ∠BCD = 180°-100°
• ⇒ ∠BCD = 80°

∴ The measure of ∠BCD = 80°.