Skill: Identify supplementary angles

Two angles are supplementary if their measures add to $(180^\circ)$:

$$m\angle A+m\angle B=180^\circ$$

They may be next to each other, or they may be separate. If they are adjacent and their outside sides form a straight line, they are called a linear pair.

Example:
In a diagram, $(m\angle 1=65^\circ)$ and $(m\angle 2=115^\circ)$. Are $\angle 1$ and $\angle 2$ supplementary?

Step 1: Add the angle measures.

$$65^\circ+115^\circ=180^\circ$$

Step 2: Compare the sum with $(180^\circ)$.

The sum is $(180^\circ)$, so the angles are supplementary.

Answer: $\angle 1$ and $\angle 2$ are supplementary angles. If they share a side and form a straight line, they also make a linear pair.

Remember: angles that add to $(90^\circ)$ are complementary, not supplementary.