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°
