Question

In a cyclic quadrilateral ABCD angle A=(2x+y),angleB=(y+3) angleC=(2y+10) angle D=(4x-5) find four angles

Answer 1

As per the rule,

=>Sum of Opposite angle of a cyclic quadrilateral is equal to 180

So, following this rule

angle A+angle C=180

2x+y+2y+10=180

2x+3y=180-10

2x+3y=170................i×2


angle B+angle D=180

y+3+4x-5=180

4x+y-2=180

4x+y=180+2

4x+y=182...............ii

sub ii from i×2

4x+6y-(4x+y)=340-182

4x+6y-4x-y=158

5y=158

y=158/5

putting value of y in equation ii

4x+y=182

4x+158/5=182

(20x+158)/5=182

20x+158=910

20x=910-158

20x=752

x=752/20

x=376/10