Question

find x and y i need a perfect solution

Answer 1

Triangle ABC seems Isosceles,
Therefore, Triangle OBC is also Isosceles(as it is aligned to the bigger triangle)
In Triangle OBC,
The base angles should be equal.
Therefore, y=37°
For x,
37°+37°+x=180°
74°+x=180°
x=180°-74°
=>x=106°
Hope it helps you.

Answer 2

At first let us consider the triangle ABC,

Using the angle sum property of triangle,

∠A + ∠B +∠C=180°

55°+22°+37°+∠C=180°

114°+∠C=180°

∠C=66°

From figure , ∠C=∠y+∠y

∠C=2∠y

66°=2∠y

∠y=66°/2=33°

∠y=33°....................... (1)

Now consider triangle OBC

Using angle sum property, ∠O +∠B+∠C=180°

∠x+∠y+37°=180°

plugging value of ∠y from equation 1

∠x+33°+37°=180°

∠x=180°-70°=110°

Answer ∠y=33° and ∠=110°