We know that the sum of linear pair are always equal to 180°

POY + a + b = 180°

Putting the value of POY = 90° (as given in the question) we get,

a + b = 90°

Now, it is given that a : b = 2 : 3

Let a be 2x and b be 3x

∴ 2x + 3x = 90°

Solving this we get

5x = 90°

x = 18°

∴ a = 2 × 18° = 36°

Similarly, b can be calculated and the value will be

b = 3×18° = 54°

From the diagram, b + c also forms a straight angle so,

b + c = 180°

c+54° = 180°

∴ c = 126°