Question

In the given figure, $\angle ABC={69}^{\circ }$ and $\angle ACB={31}^{\circ }.$ Find $\angle BDC.$

• A. ${60}^{\circ }$
• B. ${70}^{\circ }$
• C. ${100}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

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

Given that $\angle ABC={69}^{\circ }$ and $\angle ACB={31}^{\circ }.$
Using angle sum property in $△ABC,$ we have
$\angle BAC+\angle ABC+\angle ACB={180}^{\circ }.$
i.e., $\angle BAC+{69}^{\circ }+{31}^{\circ }={180}^{\circ }$
$⟹\angle BAC={180}^{\circ }-{100}^{\circ }={80}^{\circ }$
Now, since the angles in the same segment are equal,
$\angle BAC=\angle BDC.$
$\therefore \angle BDC={80}^{\circ }$