In \(\triangle ABC\), the bisectors of \(\angle B\) and \(\angle C\) meet at a point O inside the triangle. If \(\angle BOC=106^\circ\), what is the measure of \(\angle A\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 32°
In \(\triangle BOC\) the angles at B and C are half of \(\angle B\) and half of \(\angle C\), and the angles of every triangle add up to \(180^\circ\).
\(\angle OBC+\angle OCB=180^\circ-106^\circ=74^\circ\)
So \(\frac{1}{2}(\angle B+\angle C)=74^\circ\), giving \(\angle B+\angle C=148^\circ\)
\(\angle A=180^\circ-148^\circ=32^\circ\)
