Quantitative Aptitude Ques 77
Question: If I is the in centre of $ \Delta ABC $ and $ \angle BIC=135{}^\circ , $ then $ \Delta ABC $ is
Options:
A) acute angled
B) equilateral
C) right angled
D) obtuse angled
Show Answer
Answer:
Correct Answer: C
Solution:
- $ \because \angle BIC=135{}^\circ $ In $ \Delta BIC, $ $ \angle BIC+\angle IBC+\angle ICB=180{}^\circ $
$ \Rightarrow $ $ \angle IBC+\angle ICB=180{}^\circ -135{}^\circ =45{}^\circ $
$ \Rightarrow $ $ 2\angle IBC+2\angle ICB=90{}^\circ $
$ \Rightarrow $ $ \angle B+\angle C=90{}^\circ $ Now, $ \angle A+\angle B+\angle C=180{}^\circ $
$ \therefore $ $ \angle A=90{}^\circ $ Hence, $ \Delta ABC $ is a right angled triangle.
BETA
