Question

The external bisectors of $\angle B$ and $\angle C$ of $\Delta ABC$, meet in O. If $\angle A$ is equal to ${50}^o$, then the magnitude of $\angle BOC$ is:

• A. ${140}^o$
• B. ${105}^o$
• C. ${65}^o$
• D. ${60}^o$

Answer 1

Answer: (C)

${65}^o$

We have the formula,

Two sides $AB$ & $AC$ of $△ABC$ are produced to $P$ & $Q$ respectively. If the bisectors of $\angle PBC$ & $\angle QCB$ intersect each other at $O$, then,

$\angle BOC={90}^{\circ }-\frac{1}{2}\times \angle A$

$\angle BOC={90}^{\circ }-\frac{1}{2}\times {50}^{\circ }$

$\angle BOC={90}^{\circ }-{25}^{\circ }$

$\angle BOC={65}^{\circ }$