Question

abcd is a cyclic quadrilateral find the values of X and y

Answer 1

Hey there,

In a cyclic quadrilateral, sum of opposite angles=180 degrees.
So,

2x+4+4y-4=180
x+2y=90

and

x+10+5y+5=180
x+5y=165

So we get-
x=40
y=25

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Answer 2

A cyclic quadrilateral is a quadrilateral in which all the vertices touch a circle.

The sum of opposite angles of a cyclic quadrilateral is $180^\circ$

Explanation:

$ABCD$ is a cyclic quadrilateral.

So, $\angle A+\angle C=180^\circ$ and $\angle B+\angle D=180^\circ$

$\implies 2x+4+4y-4=180$

$\implies 2x+4y=180$

$\implies x+2y=90$   ..........(1)

Also,

$\implies x+10+5y+5=180$

$\implies x+5y+15=180$

$\implies x+5y=165$   .........(2)

Subtracting eq(2) and (1)

$\implies x+5y-(x+2y)=165-90$

$\implies x+5y-x-2y=165-90$

$\implies 3y=75$

$\implies y=25$

Substituting in (1)

$\implies x+2(25)=90$

$\implies x+50=90$

$\implies x=40$

Hence the value of $x=40,y=25$