A) \[36{}^\circ \]
B) \[72{}^\circ \]
C) \[24{}^\circ \]
D) \[48{}^\circ \]
Correct Answer: A
Solution :
Let the angles of quadrilateral are x, 2x, 3x and 4x respectively. So, \[x+2x+3x+4x=360{}^\circ \] \[10x=360{}^\circ \] \[x=360{}^\circ \] \[\therefore \] Smallest angle of triangle \[=\,\,\,\,\,\frac{2}{3}\times 36{}^\circ =24{}^\circ \] Largest angle of triangle \[=5\times 24{}^\circ =~120{}^\circ \] \[\therefore \] Second largest angle of triangle \[=\,\,\,\,180{}^\circ -(24{}^\circ +120{}^\circ )\] \[=\,\,\,\,180{}^\circ -144{}^\circ \] \[=\,\,\,\,36{}^\circ \]
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