Question

In the figure $AD||BC;\angle CAB={45}^{\circ };\angle DBC={55}^{\circ }$, then $\angle DCB$ equals:

• A. ${55}^{\circ }$
• B. ${80}^{\circ }$
• C. ${100}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

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

Here, $\angle DAC=\angle DBC={55}^o$ ...(angles in the same segment).

Then, $\angle DAB=\angle DAC+\angle CAB={55}^o+{45}^o={100}^o$.

Now, $\angle DAB+\angle DCB={180}^o$ ...(opposite angles of cyclic quadrilateral $ABCD$)

$\Rightarrow \angle DCB={180}^o-{100}^o={80}^o$.

Therefore, option $B$ is correct.