(Q23).Two angles are complementary. The larger angle is 3° less than twice the measure of the smaller angle. Find the measure of each angle.

Let the pair of complementary angles be x° and y°

with x° > y°

then x° + y° = ° and

By problem

x = y – ° ⇒ x – y = – °

Solving these two equations we get,

x +     y =

x - y = -

y =
∴ y =
= °

Substituting y = °in x + y = 90° we get

x + ° = 90°

⇒ x = 90° – ° = °

The angles are ° and °.