An angle is 30° more than one half of its complement. Find difference between the greater and the smaller angles.

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

We know that,

Sum of complementary angles = 90o

⇒ x + y = 90o

⇒ y = 90o - x

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

⇒ y = x/2 + 30o

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

⇒ 60o = 3x/2

⇒ x = 120°/3 = 40o

Then,

⇒ y = 90o - 40o = 50o

Difference between the greater and the smaller angles

⇒ y - x = 50o - 40o = 10o

∴ The difference between the greater and the smaller angles = 10o