Question

If one of the angles of a triangle is ${130}^o$, then the angle between the bisectors of the other two angles can be:

• A. ${50}^o$
• B. ${65}^o$
• C. ${145}^o$
• D. ${155}^o$

Answer 1

The correct option is D ${155}^o$

Consider a $△ABC$,such that $\angle BAC={130}^{\circ }$ and bisectors of $\angle B$ and $\angle C$ meet at $O$.
To find: $\angle BOC$
Now, in $△ABC$,
$\angle BAC+\angle ABC+\angle ACB=180$
$130+\angle ABC+\angle ACB=180$ (Angle sum property)
$\angle ABC+\angle ACB=50$
$\frac{1}{2}(\angle ABC+\angle ACB)=25$
$\angle OBC+\angle OCB=25$ (OB and OC bisect $\angle ABC$ and $\angle ACB$)
Now, in $△OBC$,
$\angle OBC+\angle OCB+\angle BOC=180$
$25+\angle BOC=180$
$\angle BOC={155}^{\circ }$.