Question

Please solve as soon as possible.....

Answer 1

Hello!

Steps in the attachment.

Thank You!

Answer 2

Answer:

∠A = 120°

∠B = 70°

∠C = 60°

∠D = 110°

Hope this helps you!

Step-by-step explanation:

Since opposite angles of a cyclic quadrilateral are supplementary (add up to 180°), we have

∠A + ∠C = 180°

=> (4y+20) + 4x = 180

=> 4x + 4y = 160

=> x + y = 40       .... (1)

Also

∠B + ∠D = 180°

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

=> 7x + 3y = 180       .... (2)

From (1), we get y = 40 - x.  Substituting this into (2) gives

7x + 3(40-x) = 180

=> 7x + 120 - 3x = 180

=> 4x = 60

=> x = 15

and y = 40 - x = 40 - 15 = 25.

The four angles are then

∠A = (4y+20)° = 120°

∠B = (3y-5)° = 70°

∠C = (4x)° = 60°

∠D = (7x+5)° = 110°