| 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] |
A) \[160{}^\circ \]
B) \[180{}^\circ \]
C) \[190{}^\circ \]
D) \[170{}^\circ \]
E) None of these
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 \[=120{}^\circ +60{}^\circ =180{}^\circ \] |
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