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

**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 "x" and 41° are complementary angles, 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 "x" and 62° are complementary angles, we have

x + 62° = 90°

x = 90° - 62°

x = 28°

**Hence the measure of the complementary angle is 28°**

**Example 3 :**

The measure of an angle is 108°. What is the measure of a supplementary angle?

**Solution :**

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

Since "x" and 108° are supplementary angles, we have

x + 108° = 180°

x = 180° - 108°

x = 72°

**Hence the measure of the supplementary angle is 72°**

**Example 4 :**

The measure of an angle is 89°. What is the measure of a supplementary angle?

**Solution :**

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

Since "x" and 41° are supplementary angles, we have

x + 89° = 180°

x = 180° - 89°

x = 91°

**Hence the measure of the supplementary angle is 91°**

**Example 5 :**

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

x + 2x = 90°

3x = 90°

x = 30° and 2x = 60°

**Hence the two angles are 30° and 60°**

**Example 6 :**

Two angles are supplementary. If one angle is two times the sum of other angle and 3, find the two angles.

**Solution :**

Let "x" and "y" be the two angles which are complementary.

So, we have x + y = 90° --------> (1)

From the information, "one angle is two times the sum of other angle and 3", we have

x = 2(y+3)

x = 2y + 6 ------->(2)

Now plug x = 2y + 6 in equation (2)

(1)-------> 2y + 6 + y = 90

3y + 6 = 90

3y = 84

y = 28

Now, plug y = 28 in equation (2).

(2) --------> x = 2(28) + 6

x = 56 + 6

x = 62

**Hence the two angles are 62° and 28° **

**Example 7 :**

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

x + 45° = 90°

x = 90° - 45°

x = 45°

**Hence the measure of the complementary angle is 45°**

**Example 8 :**

Two angles are supplementary. If one angle is 36° less than twice of the other angle, find the two angles.

**Solution :**

Let "x" and "y" be the two angles which are supplementary.

So, we have x + y = 180° ----------->(1)

From the information, "one angle is 36

From the information, "one angle is 36° less than twice of the other angle", we have

x = 2y - 36 ----------->(2)

Now plug x = 2y - 36 in equation (1)

(1)-------> 2y - 36 + y = 180

3y - 36 = 180

3y = 216

y = 72

Now, plug y = 72 in equation (2).

(2) --------> x = 2(72) - 36

x = 144 - 36

x = 108

**Hence the two angles are 108° and 72° **

**Example 9 :**

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 "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 10 :**

Two angles are supplementary. If 5 times of one angle is 10 times of the other angle. Find the two angles.

**Solution :**

Let "x" and "y" be the two angles which are supplementary.

So, we have x + y = 180° -------->(1)

From the information, "5 times of one angle is 10 times of the other angle", we have

5x = 10y =====> x = 2y ---------(2)

Plug x = 2y in equation (1)

2y + y = 180

3y = 180

y = 60

Plug y = 60 in equation (2)

x = 2(60)

x = 120

**Hence the two angles are 60° and 120****°.**

So far we have done problems on complementary and supplementary angles without any picture.

Now, let us do some problems on complementary and supplementary angles with figures.

**Example 11 :**

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

**Solution :**

From the picture above, it is very clear (5x+4), (x-2) and (3x+7) are supplementary angles.

So, we have (5x+4) + (x-2) + (3x+7) = 180°

5x + 4 + x -2 + 3x + 7 = 180°

9x + 9 = 180

9x = 171

x = 19

**Hence the value of "x" is 19**

**Example 12 :**

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

**Solution :**

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

So, we have x + 2x = 90°

3x = 90°

x = 30°

**Hence the value of "x" is 30°**

After having gone through the problems on complementary and supplementary angles, we hope that the students would have understood "How to do problems on complementary and supplementary angles".

**To know more about problems on complementary and supplementary angles, please click here**

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