Question

20. (4) In cyclic quadrilateral ( A B C D ), ( angle A+angle C=180^{circ} )
( Rightarrow quad 4 x+5 y=180^{circ} )
(i)
and ( angle B+angle D=180^{circ} )
( Rightarrow quad 7 x+y=180^{circ} )
(ii)
From Eqs. (i) and (ii), we get ( 4 x+5 y=7 x+y )
( Rightarrow quad 3 x=4 y )
( Rightarrow quad x: y=4: 3 )

# 20. In a cyclic quadrilateral ABCD, ZA = 4x°, ZB = 7xº, ZC = 5yº and ZD = yº. Find the ratio y :x. (1) 2:3 (2) 3:2 (3) 3:4 (4) 4:3

Solution