**Complementary Angles :**

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

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°.

**Supplementary Angles :**

If the sum of two angles is 180⁰, then those two angles are called as supplementary angles.

Example :

120° and 60° are supplementary angles.

Because,

120° + 60° = 180°

Clearly, 120° is the supplement of 60° and 60° is the supplement of 120°.

**Question 1 :**

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

**Answer :**

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°.

**Question 2 :**

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

**Answer :**

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°.

**Question 3 :**

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

**Answer :**

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°.

**Question 4 :**

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

**Answer :**

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°.

**Question 5 :**

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

**Answer :**

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°.

**Question 6 :**

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

**Answer :**

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°.

**Question 7 :**

Find the value of x :

**Answer :**

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.

**Question 8 :**

Find the value of x :

**Answer :**

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.

**Question 9 :**

Find the value of x :

**Answer :**

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.

**Question 10 :**

Find the value of x :

**Answer :**

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.

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