Question

In $\Delta ABC$, the angle bisectors of $\angle B$ and $\angle C$ meet at O. If$\angle A={70}^o$, find $\angle BOC$

Answer 1

In $△BOC$,
$\angle BOC+\angle OBC+\angle OCB=180$ (OB and OC bisect $\angle B$ and $\angle C$ respectively)
$\angle BOC+\frac{1}{2}\angle B+\frac{1}{2}\angle C=180$
$\angle BOC=180-\frac{1}{2}(\angle B+\angle C)$
$\angle BOC=180-\frac{1}{2}(180-\angle A)$
$\angle BOC=180-\frac{1}{2}(180-70)$
$\angle BOC=180-90+35$
$\angle BOC={125}^{\circ }$