Question

ABCD is a cyclic quadrilateral in which angle A is equal to 2 X + Y angle b is equal to 2 X + 2 Y angle C is equal to 3 X + 2 Y angle d is equal to 4 x-2 Y find the four angles

Answer 1

Step-by-step explanation:

As we know that sum of opposite angles of a cyclic quad. is 180°

So, Angle A + Angle C = 180°

Similarly, Angle B + Angle D =180°

Now, A+C = B+ D

Putting the values of ABCD IN the equation

2x+y + 3x+2y = 2x+2y + 4x-2y

5x+3y = 6x = 180°

Now x = 180/6 = 30

Also 5x+3y=180°

So, 5(30) +3y =180

150 +3y =180

3y = 180-150

3y =30

y = 10

now

A= 2(30)+ 10 =70

B = 2(10) + 2(30) = 80

C = 3(30)+2(10)=110

D = 4(30)-2(10)=100