question_answer

If ABCD be a cyclic quadrilateral in which \[\angle A=4x{}^\circ ,\]\[\angle B=7x{}^\circ ,\]\[\angle C=5y{}^\circ ,\]\[\angle D=y{}^\circ ,\]then \[x:y\]is                                         [SSC (CGL) Mains 2014]

A) 3 : 4                 

B) 4 : 3  

C) 5 : 4                             

D) 4 : 5

Correct Answer: B

Solution :

In a cyclic quadrilateral.

Sum of opposite angle \[=180{}^\circ \]

So, \[4x+5y=7x+y=180{}^\circ \]

\[\Rightarrow \]\[4x+5y=7x+y\]

\[\Rightarrow \]\[5y-y=7x-4x\]

\[\Rightarrow \]\[4y=3x\]\[\Rightarrow \]\[\frac{4}{3}=\frac{x}{y}\]

\[\therefore \]\[x:y=4:3\]