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 quadrilaterals 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 to the quadrilateral? [Bank of Baroda (PO) 2011]
Options:
A) $ 160{}^\circ $
B) $ 180{}^\circ $
C) $ 190{}^\circ $
D) $ 170{}^\circ $
E) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- Here/ratio among the angles of quadrilateral
= 3: 4: 5: 6
Now, total sum of the angles of quadrilateral $ =360{}^\circ $
$ \Rightarrow $ $ (3+4+5+6)x=360{}^\circ $
$ \Rightarrow $ $ x=\frac{360{}^\circ }{18} $
$ \Rightarrow $ $ x=20{}^\circ $
Largest angle of quadrilateral $ =6\times 20{}^\circ =120{}^\circ $
Smallest angle of quadrilateral
$ 3\times 20{}^\circ =60{}^\circ $
Now, smallest angle of triangle $ =\frac{2}{3}\times 60{}^\circ =40{}^\circ $
$ \therefore $ Largest angle of triangle $ =2\times 40{}^\circ =80{}^\circ $
$ \therefore $ Second largest angle of triangle
$ =180{}^\circ -(80{}^\circ +40{}^\circ ) $
$ =180{}^\circ -120{}^\circ =60{}^\circ $
$ \therefore $ Required sum $ =120{}^\circ +60{}^\circ =180{}^\circ $
BETA
