Question: Smallest angle of a triangle is equal to two-third 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?
Options:
A) $ 160{}^\circ $
B) $ 180{}^\circ $
C) $ 190{}^\circ $
D) $ 170{}^\circ $
E) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- Let the angles of the quadrilateral be $ 3x, $ $ 4x, $ $ 5x $ and $ 6x, $ respectively.
Then, $ 3x+4x+5x+6x=360{}^\circ $
$ \Rightarrow $ $ 18x=360{}^\circ $
$ \Rightarrow $ $ x=20{}^\circ $
$ \therefore $ Smallest angle of quadrilateral $ =3x=60{}^\circ $
$ \therefore $ Smallest angle of the triangle $ =60{}^\circ \times \frac{2}{3}=40{}^\circ $
$ \therefore $ Largest angle of the triangle $ =40{}^\circ \times 2=80{}^\circ $
$ \therefore $ Second largest angle of the triangle $ =60{}^\circ $
$ \therefore $ Sum of the second largest angle of triangle and
largest angle of quadrilateral $ =60{}^\circ +6\times 20{}^\circ $
$ =60{}^\circ +120{}^\circ =180{}^\circ $
BETA
