Question

If ABCD is a cyclic quadrilateral , find the angles of this cyclic quadrilateral....​

Answer 1

$\bf\large\underline\pink{Solution:-}$

3y-5-7x+5=180

3y-7x=180----------1

4y+20-4x=180

4y-4x=160

dividing each term by 4

y-x=40

y=40+x-------------2

putting 1 in2

3(40+x)-7x=180

120+3x-7x=180

-4x=60

x= -15

y=40-15

=25

so,

A=4*25 +20

=120

B=3*25-5

=70

C=-4*-15

=60

D=-7*-15+5

=110

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Answer 2

Step-by-step explanation:

In a cyclic quadrilateral, opposite angles are supplementary

thus angle A+angleC=180°

=>4y+20-4x=180

=>4y-4x=160

=>y-x=40-----1

and similarly

angle B+angleD=180

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

=>3y-7x=180------2

*see the solve in the pic *

we get x=-15 and y=25

now put values of X and y

angle A=4y+20=4*25+20=120°

angle B=3y-5=3*25-5=75-5=70°

angle C=-4x=-4(-15)=60°

angle D=-7x+5=-7(-15)+5=105+5=110°