# PROBLEMS ON COMPLEMENTARY ANGLES

## About "Problems on complementary angles"

On this web page, we are going to have  problems on complementary angles.

Before that, do you want to know the basic stuff about "complementary and supplementary angles" ?,

Now, let us look at some problems on complementary angles.

## 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  problems on complementary angles, we hope that the students would have understood, "How to do problems on complementary angles".