Ratio And Proportion Ques 5
Question-
Smallest angle of a triangle is equal to two-third of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is $3: 4: 5: 6$. Largest angle of the triangle is twice its smallest angle. What is the sum of second largest angle of the triangle and largest angle of the quadrilateral?
(1) $160^{\circ}$
(2) $180^{\circ}$
(3) $190^{\circ}$
(4) $170^{\circ}$
(5) None of these
(Bank Of Baroda PO Exam. 13.03.2011)
Show Answer
Correct Answer: (2)
Solution: (2)
Sum of the angles of quadrilateral $=360^{\circ}$
$\therefore 3 x+4 x+5 x+6 x=360$
$\Rightarrow 18 x=360$
$\Rightarrow x=\frac{360}{18}=20$
$\therefore$ Smallest angle of quadrilateral $=3 \times 20=60^{\circ}$
Largest angle of quadrilateral $=6 \times 20=120^{\circ}$
$\therefore$ Smallest angle of triangle $=60 \times \frac{2}{3}=40^{\circ}$
Largest angle of triangle $=2 \times 40=80^{\circ}$
$\therefore$ Third angle of triangle $=180^{\circ}-40^{\circ}-80^{\circ}=60^{\circ}$
$\therefore$ Required sum $=60+120=180^{\circ}$
BETA
