### Supplementary Angles, Properties, Examples and Solution

Angles are Supplementary Angle if Sum Of Two Angles 180 degrees. These two angles (135° and 45°) are Supplementary Angle, because sum of 135°+45°=180°.- Supplementary Angles together make a straight line, But the angles don't have to be together.

- When the two angles sum 180°, they "Supplement" each other.

- When two adjacent angles form a straight line, they are supplementary.

- If one angle is known, its supplementary angle can be found by subtracting the measure of its angle from 180°.

Fig 1 Example of Supplementary Angles, because sum of angle a and b are 180°.

Fig 1: Supplementary Angles |

**Determine supplement Angle**To determine the Supplement, subtract the given angle from 180.

Example 1:If one angle is 50 degree, find the second angle if the two angles are supplementary to each other.Solution:180 - 50 = 130°, The Supplement of 50° is 130°.

Example 2:If one angle is 60 degree, find the second angle if the two angles are supplementary to each other.Solution:180 - 60 = 120° , The Supplement of 60° is 120°.

Example 3:If one angle is 30 degree, find the second angle if the two angles are v to each other.Solution:180 - 30 = 150°, The Supplement of 30° is 150°.

Example 4:If one angle is 15 degree, find the second angle if the two angles are supplementary to each other.Solution:180 - 15 = 165° , The Supplement of 15° is 165°.

**Some other examples of supplementary angle pairs**

20 degrees and 160 degrees

40 degrees and 140 degrees

60 degrees and 120 degrees

70 degrees and 110 degrees

90 degrees and 90 degrees**Practice Problems**

**Example**

**1:**The measure of angle 1 is 27 degree and angle 2 is 150 degree. Identify whether the angles are supplementary to each other or not?

**Example 2:**Let first angle is 12 degrees, find the second angle if the two angles are supplementary to each other?

**Example 3:**x and y are supplementary angles. Given x = 45˚, find the value y?

**Example**

**4:**The measure of angle 1 is 27 degree and angle 2 is 150 degree. Identify whether the angles are supplementary to each other or not?

**Example 5:**Let first angle is 22 degrees, find the second angle if the two angles are supplementary to each other?

**Example**

**6:**The measure of angle 1 is 10 degree and angle 2 is 120 degree. Identify whether the angles are supplementary to each other or not?

**Example 7:**Let first angle is 120 degrees, find the second angle if the two angles are supplementary to each other?

**Example**

**8:**The measure of angle 1 is 15 degree and angle 2 is 145 degree. Identify whether the angles are supplementary to each other or not?

**Example 9:**Let first angle is 12 degrees, find the second angle if the two angles are supplementary to each other?

**Example**

**10:**The measure of angle 1 is 30 degree and angle 2 is 135 degree. Identify whether the angles are supplementary to each other or not?

**Practice Problems for Home Work**

**Example 1 :**The measure of angle 1 is 27 degree and angle 2 is 150 degree. Identify whether the angles are supplementary to each other or not?

**Example 2 :**Let first angle is 12 degrees, find the second angle if the two angles are supplementary to each other?

**Example 3 :**x and y are supplementary angles. Given x = 45˚, find the value y