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, \[4x+5y=7x+y=180{}^\circ \] |
\[\Rightarrow \]\[4x+5y=7x+y\] |
\[\Rightarrow \]\[5y-y=7x-4x\] |
\[\Rightarrow \]\[4y=3x\]\[\Rightarrow \]\[\frac{4}{3}=\frac{x}{y}\] |
\[\therefore \]\[x:y=4:3\] |
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