Question

In the given figure,$\angle ABD={70}^{\circ },\angle ADB={30}^{\circ }$.Then $\angle BCD$ is

• A. ${60}^{\circ }$
• B. ${80}^{\circ }$
• C. ${100}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is C ${100}^{\circ }$

In $△ABD,$

$\angle ABD+\angle BDA+\angle DAB={180}^{\circ }$ by angle sum property

$\Rightarrow \angle DAB={180}^{\circ }-(\angle ABD+\angle BDA)$

$\Rightarrow \angle DAB={180}^{\circ }-({70}^{\circ }+{30}^{\circ })$

$\Rightarrow \angle DAB={180}^{\circ }-{100}^{\circ }={80}^{\circ }$

$\angle BAD$ and $\angle BCD$ are supplementary angles

$\therefore \angle BCD={180}^{\circ }-\angle BAD={180}^{\circ }-{80}^{\circ }={100}^{\circ }$