Question

In the given figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If $\angle DBC={55}^{\circ }$ and $\angle BAC={45}^{\circ }$, then $\angle BCD$ = ___ .

• A. ${80}^{\circ }$
• B. ${70}^{\circ }$
• C. ${60}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is A ${80}^{\circ }$

Note that $\angle CAD=\angle DBC={55}^{\circ }.$ (Angles in the same segment)
Thus, $\angle DAB=\angle CAD+\angle BAC={55}^{\circ }+{45}^{\circ }={100}^{\circ }.$
But, $\angle DAB+\angle BCD={180}^{\circ }.$ (Opposite angles of the cyclic quadrilateral ABCD)
So, $\angle BCD={180}^{\circ }–{100}^{\circ }={80}^{\circ }.$