Two angles are complementary. Their difference is 34 degrees. Find the angles.

Question

can i see this in equation form? using variables for the angles

Answer 1

When two angles are complementary, the sum of their angles is 90 degrees.

 

Let one angle = x

Let other angle = y

 

 

Set up two equations.

 

x + y = 90       eq1

x - y = 34        eq2

 

 

Subtract the equations to eliminate the x terms.

 

2y = 56

 y = 28

 

 

Substitute this value of y into eq1.

 

x = 90 - y

x = 90 - 28

x = 62

 

The two angles are 62 degrees and 28 degrees.

 

Let's check these values to make sure they satisfy the conditions in the question.

 

62 + 28 = 90

      90   = 90

 

True.

 

62 - 28 = 34

     34   = 34

 

True.

 

They check out.