Supplementary and complementary angles

Chapter 5 Class 7 Lines and Angles
Concept wise

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°