Ratio And Proportion Ques 4
Question-
One of the angles of a quadrilateral is thrice the smaller angle of a parallelogram. The respective ratio between the adjacent angles of the parallelogram is $4: 5$. Remaining three angles of the quadrilateral are in ratio $4: 11: 9$ respectively. What is the sum of the largest and the smallest angles of the quadrilateral?
(1) $255^{\circ}$
(2) $260^{\circ}$
(3) $265^{\circ}$
(4) $270^{\circ}$
(5) None of these
(UCO Bank PO Exam. 30.01.2011)
Show Answer
Correct Answer: (2)
Solution: (2)
For the Parallelogram,
$4 x^{\circ}+5 x^{\circ}=180^{\circ}$
$\Rightarrow 9 x=180 $
$\Rightarrow x=\frac{180}{9}=20$
$\Rightarrow$ smaller angle of parallelogram $=4 \times 20=80^{\circ}$
$\therefore$ One angle of the quadrilateral $=3 \times 80=240^{\circ}$
Now,
$4 y+11 y+9 y$ $=360-240=120$
$\Rightarrow 24 y=120 $
$\Rightarrow y=\frac{120}{24}=5$
$\Rightarrow$ Its smallest angle $=4 \times 5=20^{\circ}$
$\therefore$ Required sum $=240^{\circ}+20^{\circ}=260^{\circ}$
BETA
