Question

In the figure aove, $C$ is the intersection of $\overline{AD}$ and $\overline{BE}$. If it can be determined, what is the measure of $\angle BAC$?

• A. ${80}^o$
• B. ${100}^o$
• C. ${110}^o$
• D. ${115}^o$
• E. Cannot be determined from the given information

Answer 1

The correct option is B ${100}^o$

$\angle BCA=\angle DCE$ (Vertically opposite angles)

$\Rightarrow \angle BCA={45}^{\circ }$

Now in $△ABC$ using angle sum property

$\angle BAC+\angle CBA+\angle BCA={180}^{\circ }$

$\Rightarrow \angle BAC+{35}^{\circ }+{45}^{\circ }={180}^{\circ }\Rightarrow \angle BAC={180}^{\circ }-{80}^{\circ }\Rightarrow \angle BAC={100}^{\circ }$