**Complementary and Supplementary Angles Worksheet Pdf :**

Worksheet given in this section will be much useful for the students who would like to practice problems on complementary and supplementary angles.

Before look at the worksheet, if you would like to learn about complementary and supplementary angles,

To download complementary and supplementary angles worksheet as pdf document,

**Problem 1 :**

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

**Problem 2 :**

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

**Problem 3 :**

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

**Problem 4 :**

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

**Problem 5 :**

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

**Problem 6 :**

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

**Problem 7 :**

Find the value of x :

**Problem 8 :**

Find the value of x :

**Problem 9 :**

Find the value of x :

**Problem 10 :**

Find the value of x :

**Problem 1 :**

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

**Solution :**

Let x be the measure of the required complementary angle.

Because x and 41° are complementary angles,

x + 41° = 90°

Subtract 41° from each side.

x = 49°

So, the measure of the complementary angle is 49°.

**Problem 2 :**

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

**Solution :**

Let x be the measure of the required complementary angle.

Because x and 62° are complementary angles,

x + 62° = 90°

Subtract 62° from each side.

x = 28°

So, the measure of the complementary angle is 28°.

**Problem 3 :**

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

**Solution :**

Let x be the measure of the required supplementary angle.

Because x and 108° are supplementary angles,

x + 108° = 180°

Subtract 108° from each side.

x = 72°

So, the measure of the supplementary angle is 72°.

**Problem 4 :**

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

**Solution :**

Let x be the measure of the required supplementary angle.

Because x and 41° are supplementary angles,

x + 89° = 180°

Subtract 89° from each side.

x = 91°

So, the measure of the supplementary angle is 91°.

**Problem 5 :**

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 is 2x.

Because x and 2x are complementary angles, we have

x + 2x = 90°

3x = 90

Divide each side by 3.

x = 30

And,

2x = 2(30) = 60

So, the two angles are 30° and 60°.

**Problem 6 :**

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)

**Given :** One angle is two times the sum of other angle and 3.

Then,

x = 2(y + 3)

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

Now, substitute (2y + 6) for x in (1).

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

3y + 6 = 90

Subtract 6 from each side.

3y = 84

Divide each side by 3.

y = 28

Substitute 28 for y in (2).

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

x = 56 + 6

x = 62

So, the two angles are 62° and 28°.

**Problem 7 :**

Find the value of x :

**Solution :**

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

Then,

x + 2x = 90

Simplify.

3x = 90

Divide each side by 3.

x = 30

So, the value of x is 30.

**Problem 8 :**

Find the value of x :

**Solution :**

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

Then,

(x+1) + (x-1) + (x+3) = 90

x + 1 + x - 1 + x + 3 = 90

Simplify.

3x + 3 = 90

Subtract 3 from each side.

3x = 87

Divide each side by 3.

x = 29

So, the value of x is 29.

**Problem 9 :**

Find the value of x :

**Solution :**

From the picture above, it is clear that (2x+3) and (x-6) are supplementary angles.

Then,

(2x+3) + (x-6) = 180

2x + 3 + x - 6 = 180

Simplify.

3x - 3 = 180

Add 3 to each side.

3x = 183

Divide each side by 3.

x = 61

So, the value of x is 61.

**Problem 10 :**

Find the value of x :

**Solution :**

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

Then,

(5x+4) + (x-2) + (3x+7) = 180

5x + 4 + x -2 + 3x + 7 = 180

Simplify.

9x + 9 = 180

Subtract 9 from each side.

9x = 171

Divide each side by 9.

x = 19

So, the value of x is 19.

After having gone through the stuff given above, we hope that the students would have understood complementary and supplementary angles.

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