# Measure of an Arc

How to solve the measure of an arc problems: definition, examples, and their solutions.

## Definition

The measure of an arc

is the measure of the arc's central angle.

## Example 1

m[arc *AB*] = m∠(blue) = 60

Just like this arc,

if 0 < m[arc] < 180,

then it's called the minor arc.

## Example 2

m[arc *ADB*] = m∠(blue) = 360 - 60

Just like this arc,

if 180 < m[arc] < 360,

then it's called the major arc.

## Example 3

The blue angles are congruent.

Vertical angles

So m[arc *DE*] = m∠(blue) = 60.

## Example 4

m∠(purple) + m[arc *BC*] + m∠(red) = 180

60 + m[arc *BC*] + 45 = 180