Finding complementary angles

Let’s take a example

Find complementary angle of 45°

Given angle  = 45°

We know that,

  If two angles are complementary, their sum is 90°

So,

Angle 1 + Angle 2 = 90°

45° + Angle 2 = 90°

         Angle 2 = 90° − 45°

         Angle 2 = 45°

So, complementary of 45° is 45°      

Find complementary angle of 65°

Given angle  = 65°

We know that,

  If two angles are complementary, their sum is 90°

So,

Angle 1 + Angle 2 = 90°

65° + Angle 2 = 90°

        Angle 2 = 90° − 65°

       Angle 2 = 25°

So, complementary of 65° is 25°      

Find complementary angle of 41°

Given angle  = 41°

We know that,

  If two angles are complementary, their sum is 90°

So,

Angle 1 + Angle 2 = 90°

41° + Angle 2 = 90°

        Angle 2 = 90° − 41°

        Angle 2 = 49°

So, complementary of 41° is 49°      

Find complementary angle of 54°

Given angle  = 54°

We know that,

  If two angles are complementary, their sum is 90°

So,

Angle 1 + Angle 2 = 90°

54° + Angle 2 = 90°

Angle 2 = 90° − 54°

Angle 2 = 36°

So, complementary of 54° is 36°      

The difference in the measures of two complementary angles is 12 °. Find the measures of the angles.

Let’s assume one angle be ∠1

and the other to be ∠2.  

Where ∠1 > ∠2

Now,

   ∠1 − ∠2 = 12°

   ∠1 = ∠2 + 12°

We know that,

  If two angles are complimentary, their sum is 90°

So,

  ∠1 + ∠2 = 90°

  (∠2 + 12°) + ∠2 = 90°

  ∠2 + 12° + ∠2 = 90°

  2∠2 = 90° − 12°

  2∠2 = 78°

 ∠2 = (78°)/2

 ∠2 = 39°

Now,

 ∠1 = ∠2 + 12°   

 ∠1 = 39° + 12°

 ∠1 = 51°

So, Required angles are of 51°  and 39°