# COMPLEMENTARY ANGLES

"Complementary angles"  is the much required stuff for the students who stuff math in school level.

Let us have a clear understanding about complementary-angles.

Complementary-Angles  :

If the sum of two angles is 90⁰, then those two angles are called as complementary-angles.

Example :

Example, 30° and 60° are complementary-angles.

Because 30° + 60° = 90°.

Clearly, 30° is the complement of 60° and 60° is the complement of 30°.

## Example problems

Example 1 :

The measure of an angle is 41°. What is the measure of a complementary-angle?

Solution :

Let "x" be the measure of a complementary-angle required.

Since the angles "x" and 41° are complementary, we have

x + 41° = 90°

x = 90° - 41°

x = 49°

Hence the measure of the complementary-angle is 49°

Example 2 :

The measure of an angle is 62°. What is the measure of a complementary-angle?

Solution :

Let "x" be the measure of a complementary-angle required.

Since the angles "x" and 62° are complementary, we have

x + 62° = 90°

x = 90° - 62°

x = 28°

Hence the measure of the complementary-angle is 28°

Example 3 :

Two angles are complementary. In one of the angles is double the other angle, find the two angles.

Solution :

Let "x" be one of the angles.

Then the other angle = "2x"

Since the angles "x" and "2x" are complementary, we have

x + 2x = 90°

3x = 90°

x = 30° and 2x = 60°

Hence the two angles are 30° and 60°

Example 4 :

The measure of an angle is 3/4 of 60°. What is the measure of the complementary angle ?

Solution :

Let "x" be the measure of a complementary angle required.

Given angle = 3/4 of 60° = (3/4)x60° = 3x15° = 45°

Since "the angles x" and 45° are complementary, we have

x + 45° = 90°

x = 90° - 45°

x = 45°

Hence the measure of the complementary angle is 45°

Example 5 :

An angle and its one-half are complementary. Find the angle.

Solution :

Let "x" be the required angle.

Its one half is x/2

Since the angles "x" and "x/2" are complementary, we have

x + x/2 = 90°

(2x + x)/2 = 90°

3x/2 = 90°

3x = 180°

x = 60°

Hence the required angle is 60°

Example 6 :

Find the value of  "x" in the figure given below.

Solution :

From the picture above, it is very clear that the angles "x" and "2x" are complementary.

So, we have x + 2x = 90°

3x = 90°

x = 30°

Hence the value of "x" is 30°

Example 7 :

Find the value of  "x" in the figure given below.

Solution :

From the picture above, it is very clear that the angles (x+1), (x-1) and (x+3) are complementary.

So, we have (x+1) + (x-1) + (x+3) = 90

3x + 3 = 90

3x = 87

x = 29

Hence the value of "x" is 29.

After having gone through the  stuff and examples, we hope that the students would have a clear understanding complementary-angles.

Do you want to know about supplementary angles?