Question

In the given figure $\angle A={40}^o$. If BO and CO are the bisectors of $\angle B$ and $\angle C$ respectively. Find the measure of $\angle BOC$.

Answer 1

In triangle $ABC$, applying angle sum property of triangles:

${40}^{\circ }+2x+2y={180}^{\circ }$

$2(x+y)={140}^{\circ }$

$x+y={70}^{\circ }...\left(1\right)$

Now,in triangle $ABO$,applying angle sum property of triangles:

$x+y+z={180}^{\circ }$

from equation ... (1)

${70}^{\circ }+z={180}^{\circ }$

$z={110}^{\circ }$