Question

In a cyclic quadrilateral ABC,∠A=(2x+4)⁰,∠B=(y+3)⁰, ∠C=(2y+10)⁰,∠D=(4x-5)⁰ . Find the four angles.

Answer 1

Answer:

I'm reading in 10th so I don't know this

Answer 2

∠A = 70 degrees

∠B = 53 degrees.

∠C = 110 degrees.

∠D = 127 degrees.

Step-by-step explanation:

Given: In a cyclic quadrilateral ABC,∠A=(2x+4)⁰,∠B=(y+3)⁰, ∠C=(2y+10)⁰,∠D=(4x-5)⁰ .

To Find: All the angles.

Solution: In a cyclic quadrilateral, the sum of each pair of opposite angles is 180 degrees.

So ∠A + ∠C = 180

2x + 4 + 2y + 10 = 180

2x + 2y = 166

Dividing by 2, we get x + y = 83 -----------(1)

Similarly, ∠B + ∠D = 180

y + 3 + 4x - 5 = 180

4x + y = 182 ------------(2)

Subtracting (1) from (2), we get: 3x = 99. Therefore x =  33

Substituting x = 33 in equation 1, we get 33 + y = 83. Therefore y = 50

So ∠A = 2x + 4 = 70 degrees

∠B = y + 3 = 53 degrees.

∠C = 2y+10 = 110 degrees.

∠D = 4x - 5 = 127 degrees.