Question : In $\triangle ABC$, the internal bisectors of $\angle ABC$ and $\angle ACB$ meet at $I$ and $\angle BAC=50°$. The measure of $\angle BIC$ is:
Option 1: $105°$
Option 2: $115°$
Option 3: $125°$
Option 4: $130°$
New: SSC CHSL tier 1 answer key 2024 out | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: $115°$
Solution :
Given: In $\triangle ABC$, the internal bisector of $\angle ABC$ and $\angle ACB$ meet at $I$ and $\angle BAC=50°$.
$\therefore \angle ABC+\angle ACB=180°-50°$
$⇒ \angle ABC+\angle ACB=130°$
In $\triangle BIC$,
$\angle IBC+\angle BIC +\angle ICB =180°$
$I$ is the internal bisector of $\angle ABC$ and $\angle ACB$.
$\therefore \frac{\angle ABC}{2}+\frac{\angle ACB}{2}+\angle BIC = 180°$
$⇒\angle BIC=180°-\frac{130°}{2}$
$⇒\angle BIC=180°-65°$
$⇒\angle BIC=115°$
Hence, the correct answer is $115°$.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates BrochureYour Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.