Let the smaller and greater angles be x and y respectively.

We know that,

Sum of complementary angles = 90^o

⇒ x + y = 90^o

⇒ y = 90^o - x

An angle is 30° more than one half of its complement.

⇒ y = x/2 + 30^o

⇒ 90^o – x = x/2 + 30^o   (Put the value of y = 90^o - x)

⇒ 60^o = 3x/2

⇒ x = 120°/3 = 40^o

Then,

⇒ y = 90^o – 40^o = 50^o

Difference between the greater and the smaller angles

⇒ y – x = 50^o – 40^o = 10^o