Question

(14) In cyclic quadrilateral ABCD, diagonals AC and BD intersect at P. If
Angle DBC = 70° and angle BAC = 30°, find angrBCD.
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Answer 1

Answer:

Step-by-step explanation:

<DBC=<DAC(angles in same segment)

70°=<DAC

<DAB+<BAC=180°(opposition angles are equal in cyclic quadrilateral)

<DAB=<DAC+<BAC

=70°+30°

<DAB=100

<DAB+<BAC=180°

100°+<BAC=180°

<BAC=180-100

<BAC=80°

Answer 2

Step-by-step explanation:

∠DBC = 70°, ∠BAC = 30°, then ∠BCD =?  AB = BC, then ∠ECD = ?  ∠DAC and ∠DBC are angles in same segment.  ∴ ∠DAC = ∠DBC = 70°  ∴ ∠DAC = 70°  ABCD is a cyclic quadrilateral.  ∴ Sum of opposite angles is 180°.  ∠DAB + ∠DCB = 180  100 + ∠DCB = 180  [∵ ∠DAC + ∠BAC = ∠DAB 70 + 30 = 100]  ∠DCB = 180 – 100  ∴ ∠DCB = 80  ∠DCB = ∠BCD = 80  ∴ ∠BCD = 80  In ∆ABC, AB = AC,  ∴ ∠BAC = ∠BCA = 30°  ∠BCA = 30°  ∠ECD = ∠BCD – ∠BCA = 80 – 30  ∴ ∠ECD = 50