The value of angles are ∠A = 155°, ∠B = 49°, ∠C = 160°, and ∠D = 155°.
Given that the kite has angles ∠a = (3x+5)°, ∠b = y°, ∠c = (5y-65)°, and ∠d = (4x-45)°, and that ∠a = ∠d, we can write:
3x + 5 = 4x - 45
Solving for x, we get:
x = 50
Now, we can substitute x = 50 into the equation for ∠c to find the value of y:
5y - 65 = 180
Solving for y, we get:
y = 49
Therefore, the values of the variables in the kite are x = 50 and y = 49. To find the lengths of the sides, we can substitute these values into the expressions for the sides:
Side A: ∠a = (3x+5)° = (3(50)+5)° = 155°
Side B: ∠b = y° = 49°
Side C: ∠c = (5y-65)° = (5(49)-65)° = 160°
Side D: ∠d = (4x-45)° = (4(50)-45)° = 155°
Therefore, the value of angles are are ∠A = 155°, ∠B = 49°, ∠C = 160°, and ∠D