Supplementary Angles Calculator

If you’re wondering how to calculate the supplementary angle of a given angle, don’t worry; we’ve created a special supplementary angles calculator to help you out. Calculate the supplemental angle of any desired angle with this calculator.

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If the total of two angles is 180°, they are supplementary angles. Consider a barn with a trapdoor in the floor and a hinged lid that may be opened freely. It swings through the angles a and b around the hinge until the door is fully open. Because the two angles a and b sum up to 180 degrees, they are supplementary angles. As a result, a + b = 180°. 

Supplementary Angles Calculator Use

• This online calculator is really easy to use.
• You can enter the angle value in the first field to find the supplementary angle of your desired angle.
• The calculator will then display the supplementary angle of the entered angle value when you press the calculate button.
• By clicking the reset button, you can erase the old data and calculate the supplementary angle for another angle value.

Supplementary Angles Formula

Using the formula below, you can quickly find the supplementary angle of any given angle.

Types of Supplementary Angles

The supplementary angle is primarily divided into two types:

• Adjacent Supplementary Angles
• Non-adjacent Supplementary Angles

Adjacent Supplementary Angles : Adjacent supplementary angles are defined as two supplementary angles that share a common vertex and common arm. When two supplementary angles are added together, the result is always 180°. You can use the image above as an example. ∠ABO is 140° and ∠CBO is 40° in the diagram above; If we add these angles together, we obtain 180° (140°+40°=180°). ∠ABO and ∠CBO also share a common vertex point B and a common arm BO. As a result, the two angles above are adjacent supplementary angles.

Non-adjacent Supplementary Angles : Nonadjacent supplementary angles are the opposite of adjacent supplementary angles. There is no common vertex point or arm between them. The only thing they have in common is that the total of two non-adjacent supplementary angles equals 180°. ∠PQR and ∠XYZ are separate angles that do not share a single vertex point or common arm, as seen in the above reference image, and they also add to 180° (69°+111°=180°). As a result, they are non-adjacent supplementary angles.

How to Calculate Supplementary Angles

We’ve seen that two supplementary angles add up to 180 degrees (i.e., x + y = 180°). Calculating the supplementary angle is not difficult at all. To find it, simply subtract the angle value from 180°. For example, to calculate the supplementary angle of 39°, simply subtract it from 180°, i.e 180°- 39° = 141°. Below we have some more solved examples to clear your doubts.

Example

1. Find the value of the angle X in the following figure.

Solution :

We all know that the supplementary angles add up to 180°, so subtract 105° from 180° to find the supplement angle.

Using the complementary angles formula,

Supplementary Angle (X) = 180° – angle
Supplementary Angle (X) = 180° – 105°
Supplementary Angle (X) = 75°

The value of angle X is 75°.

Example

2. Find the supplement angle of 11°

Solution :

Using the supplementary angle formula,

Supplementary Angle = 180° – angle
Supplementary Angle = 180° – 11°
Supplementary Angle = 169°

The supplementary angle of 11° is 169°

Supplementary Angles of 1° – 90°

The supplementary angles of 1° to 180° are shown in the table below.