| 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? |
A) \[160{}^\circ \]
B) \[180{}^\circ \]
C) \[190{}^\circ \]
D) \[170{}^\circ \]
E) None of these
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 \[=60{}^\circ +6\times 20{}^\circ \] |
| \[=60{}^\circ +120{}^\circ =180{}^\circ \] |
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