**Definition of Supplementary Angles**

Two angles are mentioned to be supplementary if the sum of their measures is 180°. Every angle is the complement of the opposite.

**Examples of Supplementary Angles**

The next pairs of angles are supplementary. Every pair of angles provides as much as 180°.

15°, 165°

45°, 135°

20°, 160°

72°, 108°

83°, 97°

**Extra About Supplementary Angles**

• When two strains intersect, forming 4 angles, the adjoining angles are all the time supplementary. (Adjoining angles are two angles which can be subsequent to one another.)

• Supplementary angles kind a straight angle when adjoining. (A straight angle has a measure of 180°. Straight angle varieties a straight line.)

Solved Examples on Supplementary Angles

**Instance 1**

If the measure of an angle is 59 levels, what’s the measure of its complement?

**Resolution:**

Let’s name the complement ‘x’.

“Two angles are mentioned to be supplementary if the sum of their measures is 180°.”

So:

59° + x = 180°

Subtract 59 from both sides.

59° + x – 59° = 180° – 59°

x = 121°

So, the complement of 59 levels is 121 levels.

**Instance 2**

Angles A and B are supplementary. If the measure of angle A equals the measure of angle B, then discover the measures of angles A and B.

**Resolution:**

On condition that the measure of angle A equals the measure of angle B.

Let measure of angle A = measure of angle B = x.

Angles A and B are supplementary.

“Two angles are mentioned to be supplementary if the sum of their measures is 180°.”

So:

x + x = 180°

Simplify

2x = 180°

Divide both sides by 2.

2x/2 = 180°/2

x = 90°

Due to this fact the measure of every angle is 90°.

**Instance three**

Two angles are supplementary. The angle measures are within the ratio 5:7. Discover the measure of every angle.

**Resolution:**

The angle measures are within the ratio 5:7.

So, the angle measures could be represented by 5x and 7x.

The 2 angles are supplementary.

“Two angles are mentioned to be supplementary if the sum of their measures is 180°.”

So:

5x + 7x = 180°

Simplify.

12x = 180°

Divide both sides by 12.

12x/12 = 180°/12

x = 15°

Due to this fact the angle measures are 5x = 5 × 15° = 75° and 7x = 7 × 15° = 105°.

**Instance four**

Two angles are supplementary. The bigger angle is 15 levels greater than twice the smaller angle. What are the measures of the angles?

**Resolution:**

On condition that the bigger angle is 15 levels greater than twice the smaller angle.

Let ‘x’ symbolize the measure of the smaller angle.

Then:

Measure of the bigger angle = twice the smaller angle + 15° = 2 × x + 15° = 2x + 15°

The 2 angles are supplementary.

“Two angles are mentioned to be supplementary if the sum of their measures is 180°.”

So:

Measure of bigger angle + measure of smaller angle = 180°

(2x + 15°) + x = 180°

Simplify.

3x + 15° = 180°

Subtract 15 from both sides.

3x + 15° – 15° = 180° – 15°

3x = 165°

Divide both sides by three.

3x/three = 165°/three

x = 55°

Due to this fact the measure of the smaller angle is x = 55° and the measure of the bigger angle is 2x + 15° = 2 × 55° + 15° = 110° + 15° = 125°.