"Complementary and supplementary angles word problems" is the much required stuff for the students who study math in school level.

Let us look at some complementary and supplementary angles word problems.

**Problem 1 :**

Two angles are complementary. If 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°**

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**Problem 2 :**

Two angles are complementary. 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°**

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**Problem 3 :**

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°**

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**Problem 4 :**

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°**

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**Problem 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 "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°.**

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**Problem 6 :**

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****°.**

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**Problem 7 :**

The measure of the supplement of angle A is 40 degrees larger than twice the measure of the complement of angle of A. What is the sum in degrees, of the measures of the supplement and complement of angle A ?

**Solution :**

Let "x" be the measure of angle A.

Then, supplement of angle A = 180 - x

complement of angle A = 90 - x

**Given :** (180 - x) is 40 degrees more than 2(90 - x)

So, we have

(180 - x) - 2(90 - x) = 40

180 - x - 180 + 2x = 40

x = 40

Then, supplement of angle A = 180 - x = 180 - 40 = 140

complement of angle A = 90 - x = 90 - 40 = 50

The sum of supplement and complement of angle A

= 140 + 50

= 190

**Hence the sum of supplement and complement of angle A is 190 degrees. **

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**Problem 8 :**

Twice the complement of an angle is 24 degrees less than its supplement. What is the measure of the angle ?

**Solution :**

Let "x" be the measure of angle.

Then, supplement of angle = 180 - x

complement of angle = 90 - x

**Given :** 2(90 - x) is 24 degrees less than (180 - x)

So, we have

(180 - x) - 2(90 - x) = 24

180 - x - 180 + 2x = 24

x = 24

**Hence the measure of the angle is 24 degrees. **

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**Problem 9 :**

Two angles are supplementary. If the ratio of the measure of the smaller angle to that of the larger angle is 5:7.What is the measure of the smaller angle ?

**Solution :**

From the given ratio 5 : 7,

measure of the smaller angle = 5x

measure of the larger angle = 7x

**Given :** Two angles are supplementary

5x + 7x = 180

12x = 180

Divide both sides by 12.

x = 15

Measure of the smaller angle = 5x = 5(15) = 75^{o}

**Hence the measure of the smaller angle is 75 ^{o}. **

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**Problem 10 :**

One of the measure of supplement of an angle is equal to the twice the measure of the angle. What is the measure in degrees, of the compliment of the angle ?

**Solution :**

Let "x" be the measure of the angle.

Measure of supplement of the angle = 180 - x

Measure of complement of the angle = 90 - x

**Given :** (180 - x) is equal to 2x

180 - x = 2x

180 = 3x

60 = x

Measure of the complement of angle = 90 - x = 90 - 60 = 30

**Hence the measure of compliment of the angle is 30 degrees. **

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