In \(\triangle ABC\), \(\angle A=58^\circ\). The bisectors of \(\angle B\) and \(\angle C\) meet at a point O inside the triangle. What is the measure of \(\angle BOC\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 119°
With \(\angle B+\angle C=180^\circ-\angle A\), the triangle BOC has angles \(\frac{B}{2}\) and \(\frac{C}{2}\) at B and C, which gives \(\angle BOC=90^\circ+\frac{A}{2}\).
\(\angle B+\angle C=180^\circ-58^\circ=122^\circ\)
\(\angle OBC+\angle OCB=\displaystyle\frac{122^\circ}{2}=61^\circ\)
\(\angle BOC=180^\circ-61^\circ=119^\circ\) (that is \(90^\circ+29^\circ\))
