Sequence And Series Question 621
Question: If the angles of a quadrilateral are in A.P. whose common difference is $ 10^{o} $ , then the angles of the quadrilateral are
Options:
A) $ 65^{o},,85^{o},,95^{o},,105^{o} $
B) $ 75^{o},,85^{o},,95^{o},,105^{o} $
C) $ 65^{o},,75^{o},,85^{o},,95^{o} $
D) $ 65^{o},,95^{o},,105^{o},,115^{o} $
Show Answer
Answer:
Correct Answer: B
Solution:
Suppose that $ \angle A=x^{0} $ , then $ \angle B=x+10^{o} $ , $ \angle C=x+20^{o} $ and $ \angle D=x+30^{o} $ So, we know that $ \angle A+\angle B+\angle C+\angle D=2\pi $ Putting these values, we get $ (x^{o})+(x^{o}+10^{o})+(x^{o}+20^{o})+(x^{o}+30^{o})=360^{o} $
$ \Rightarrow x=75^{o} $ Hence the angles of the quadrilateral are $ 75^{o},\ 85^{o},\ 95^{o},\ 105^{o} $ . Trick: In these type of questions, students should satisfy the conditions through options. Here B satisfies both the conditions $ i.e. $ angles are in A.P. with common difference $ 10^{o} $ and sum of angles is $ 360^{o} $ .
BETA
