In Fig. 16.189, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠ DBC =55° and ∠ BAC =45°, find ∠ BCD .

Question

In Fig. 16.189, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If &#x2220; DBC =55&#xB0; and &#x2220; BAC =45&#xB0;, find &#x2220; BCD .

Philoid · Accepted Answer

Since angles on the same segment of a circle are equal

Therefore,

∠CAD = ∠DBC = 55^o

∠DAB = ∠CAD + ∠BAC

= 55^o + 45^o

= 100^o

But,

∠DAB + ∠BCD = 180^o (Opposite angles of a cyclic quadrilateral)

Therefore,

∠BCD = 180^o – 100^o

∠BCD = 80^o

In Fig. 16.189, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC=55° and ∠BAC=45°, find ∠BCD.