| The ratio between three angles of a quadrilateral is 14: 8: 11, respectively. The value of the fourth angle of the quadrilateral is \[63{}^\circ .\] What are the sum of the largest and third largest angles of the quadrilateral? [LIC (AO) 2015] |
A) \[198{}^\circ \]
B) \[154{}^\circ \]
C) \[182{}^\circ \]
D) \[242{}^\circ \]
E) \[196{}^\circ \]
Correct Answer: A
Solution :
| The ratio between three angles of a quadrilateral is 14 : 8 : 11 and fourth angle of quadrilateral is \[63{}^\circ \] |
| Then, we know that |
| \[14x{}^\circ +8x{}^\circ +11x{}^\circ +63{}^\circ =360{}^\circ \] |
| \[\Rightarrow \] \[33x{}^\circ =297\] |
| \[\Rightarrow \] \[x{}^\circ =9{}^\circ \] |
| Then, the angles of quadrilateral are \[126{}^\circ ,\]\[72{}^\circ ,\]\[99{}^\circ \]and \[63{}^\circ \] (given). |
| \[\therefore \] Largest angle \[=126{}^\circ \] |
| Third largest angle \[=72{}^\circ \] |
| Sum \[=126{}^\circ +72{}^\circ =198{}^\circ \] |
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