Understanding Supplementary Angles: Explained and Examples

Supplementary angles

Supplementary angles are a pair of angles that add up to 180 degrees

Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if you have two angles that are supplementary, when you add their measures together, the sum will equal 180 degrees.

For example, let’s say we have angle A and angle B. If angle A measures 110 degrees, and we want to find the measure of angle B that is supplementary to angle A, we can use the equation:

angle A + angle B = 180 degrees

Substituting the given values, we get:

110 degrees + angle B = 180 degrees

To isolate angle B, we subtract 110 degrees from both sides:

angle B = 180 degrees – 110 degrees

angle B = 70 degrees

So, the measure of angle B that is supplementary to angle A is 70 degrees.

It is important to note that supplementary angles are not always adjacent. They can be anywhere in a plane as long as their sum is equal to 180 degrees. For example, angle A could be on one side of a triangle, while angle B could be on another side of the same triangle.

Supplementary angles also have some important properties. For instance, if two angles are adjacent (i.e., they share a common side and a common vertex) and are supplementary, they are referred to as a linear pair. Linear pairs are always adjacent, supplementary angles.

Additionally, if two lines intersect, the angles that are opposite each other (also known as vertical angles) are always congruent (having equal measures). Therefore, if one of the angles measures x degrees, the other angle will also measure x degrees. Since the sum of the measures of vertical angles is 180 degrees, they are always supplementary.

In conclusion, supplementary angles are a pair of angles that, when added together, give a sum of 180 degrees. They can be adjacent angles forming a linear pair or opposite angles (vertical angles) when two lines intersect.

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