Arcs

A minor arc is the shorter arc connecting two endpoints on a circle .

The measure of a minor arc is less than $180°$ , and equal to the measure of the arc's central angle .

A major arc is the longer arc connecting two endpoints on a circle.

The measure of a major arc is greater than $180°$ , and equal to $360°$ minus the measure of the minor arc with the same endpoints.

An arc measuring exactly $180°$ is called a semicircle .

In the figure, $m\stackrel{⌢}{AB}=x°$ and $m\stackrel{⌢}{ACB}=\left(360-x\right)°$ .

Note that the minor arc is named with just two endpoints, while the major arc is named with three letters, the two endpoints and a third point on the arc.

Adjacent arcs are arcs of the same circle that have exactly one point in common.

Arc Addition Postulate

The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

In the circle, $\stackrel{⌢}{PQ}$ and $\stackrel{⌢}{QR}$ are adjacent arcs.

So, $m\stackrel{⌢}{PQR}=m\stackrel{⌢}{PQ}+m\stackrel{⌢}{QR}$ .