Question

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

Answer 1

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

then x° + y° = 90° and 

By problem 

x = 2y – 3° ⇒ x – 2y = – 3°

Solving these two equations we get,

∴ y = \(\frac{93}{3}\)= 31° 

Substituting y = 31°in x + y = 90° we get 

x + 31° = 90° 

⇒ x = 90° – 31° = 59° 

The angles are 59° and 31°.