Question

find x and y of cyclic quadilateral
a=-4y+20
b=3y-5
c=-4x
d=-7x+5​

Answer 1

$\bigcirc\hspace{-4.4mm}\raise{0.5mm}\square$

Given

A cyclic quadrilateral

A=4y+20

B=3y-5

C=4x

D=-7x+5

To find

values of X and y

Solution

we know that the sum of angle of opposite side of cyclic quadrilateral is 180

Therefore ,

$\angle{A}+\angle{C}=180\degree$

=>4y+20+4x=180

=>4x+4y=160

=>X+y=40_____(1)

similarly

$\angle{D}+\angle{B}=180\degree$

=>7x+5+3y-5=180

=>7x+3y=180_____(2)

From equation (1) and (2)

Multiply by 3 in equation (1)

=>3X+3y=120_____(3)

Now from (3) and (2)

3X+3y=120

7x+3y=180

_________

-4x=-60

X=15

putting the value X in equ (1)

=>15+y=40

=>y=25

Hence,the value of X =15 and y=25