Question : In a $\triangle \mathrm{ABC}$, the bisectors of $\angle \mathrm{B}$ and $\angle \mathrm{C}$ meet at $\mathrm{O}$. If $\angle \mathrm{BOC}=142^{\circ}$, then the measure of $\angle \mathrm{A}$ is:
Option 1: $52^\circ$
Option 2: $68^\circ$
Option 3: $104^\circ$
Option 4: $116^\circ$
Correct Answer: $104^\circ$
Solution :
Given: $\angle BOC=142^\circ$
In $\triangle BOC$,
⇒ $\angle BOC+\angle OBC+\angle OCB=180^\circ$
($\because$ OB and OC bisect $\angle B$ and $\angle C$ respectively)
⇒ $\angle BOC+\frac{1}{2}\angle B+\frac{1}{2}\angle C=180^\circ$
⇒ $\angle BOC=180^\circ-\frac{1}{2}(\angle B+\angle C)$
⇒ $\angle BOC=180^\circ-\frac{1}{2}(180^\circ-\angle A)$
⇒ $\angle BOC=90^\circ+\frac{1}{2}\angle A$
⇒ $142^\circ=90^\circ+\frac{1}{2}\angle A$
⇒ $52^\circ=\frac{1}{2}\angle A$
⇒ $\angle A=104^\circ$
Hence, the correct answer is $104^\circ$.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
