**Supplementary Angles :**

Two angles are supplementary, if they add up to 90⁰.

**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°.

**Problem 1 :**

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 2 :**

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 3 :**

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 4 :**

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.

**Problem 5 :**

Two angles are supplementary. If one angle 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 supplementary angles,

x + 2x = 180°

3x = 180

Divide each side by 3.

x = 60

And,

2x = 2(60) = 120

So, the two angles are 60° and 120°.

**Problem 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 supplementary.

So, we have

x + y = 180° -----> (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 = 180

3y + 6 = 180

Subtract 6 from each side.

3y = 174

Divide each side by 3.

y = 58

Substitute 58 for y in (2).

(2)-----> x = 2(58) + 6

x = 116 + 6

x = 122

So, the two angles are 122° and 58°.

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

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