ABCD is a cyclic quadrilateral in which AC and BD are it's diagonals. Draw BC as base and AD as upper side respectively. If angle DBC=60 and angle BAC=30,find angle BCD.

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Solution

Given : angle BAC =30degree and angle DBC = 60degree
Now, angle CDB = angle BAC (angles in the same segment are equal)
therefore, angle CDB = 30degree.
In triangle BDC,
angle DBC + angle CDB + angle DCB = 180 degree (since angle sum prop)
60 degree + 30degree + angle DCB = 180 degree
angle DCB + 90degree = 180 degree
angle DCB = 180 degree - 90degree
angle DCB = 90 degree

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