Question
In given figure, $\angle A B C=69^{\circ}, \angle A C B=31^{\circ}$, find $\angle B D C$.
Image

Answer

From the given figure, in $\triangle A B C$, we can write
$\angle ABC +\angle ACB +\angle BAC =180^{\circ}  ($ by angle sum property$)$
$69^{\circ}+31^{\circ}+\angle BAC =180^{\circ}$
$\Rightarrow \angle BAC =180^{\circ}-100^{\circ}=80^{\circ}$
$\angle BDC =\angle BAC ($Angles in the same segment$)$
$\therefore \angle BDC =80^{\circ}$

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