Finding Supplementary Angles

Let’s do this by examples

Find supplementary angle of 100°

Given angle  = 100°

We know that,

  If two angles are supplementary, their sum is 180°

So,

Angle 1 + Angle 2 = 180°

100° + Angle 2 = 180°

Angle 2 = 180° − 100°

Angle 2 = 80°

So, supplementary of 100° is 80°       

Find supplementary angle of 90°

Given angle  = 90°

We know that,

  If two angles are supplementary, their sum is 180°

So,

Angle 1 + Angle 2 = 180°

90° + Angle 2 = 180°

Angle 2 = 180° − 90°

Angle 2 = 90°

So, supplementary of 90° is 90°      

Find supplementary angle of 55°

Given angle  = 55°

We know that,

  If two angles are supplementary, their sum is 180°

So,

Angle 1 + Angle 2 = 180°

55° + Angle 2 = 180°

Angle 2 = 180° − 55°

Angle 2 = 125°

So, supplementary of 55° is 125°      

Find supplementary angle of 125°

Given angle  = 125°

We know that,

  If two angles are supplementary, their sum is 180°

So,

Angle 1 + Angle 2 = 180°

    125° + Angle 2 = 180°

               Angle 2 = 180° − 125°

       Angle 2 = 55°

So, supplementary of 125° is 55°      

Among two supplementary angles, the measure of the larger angle is 44° more than the measure of the smaller. Find their measure .

Let larger angle be ∠1

and smaller angle be ∠2.  

Given,

   ∠1 = ∠2 + 44°

We know that,

If two angles are supplementary, their sum is of 180°

∴∠1 + ∠2 = 180°  

 (∠2 + 44°) + ∠2 = 180°

∠2 + 44° + ∠2 = 180°

∠2 + ∠2 = 180° − 44°

  2 × ∠2 = 136°

 ∠2 = (136°)/2

 ∠2 = 68°

Now,

  ∠1 = ∠2 + 44°  

  ∠1 = 68° + 44°

  ∠1 = 112°

So, Required angles are of 112° and 68 °