# Measure of an Arc

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

## Definition

The measure of an arc
is the measure of the arc's central angle.

## Example 1

The central angle of [arc AB], ∠AOB,
is 60º.

So m[arc AB] = 60.

When it says [arc AB],
it usually means the minor arc.

(whose measure is less than 180,
smaller than the half circle)

## Example 2

[arc ADB] is the blue arc.

This is the way to say the major arc.

(whose measure is greater than 180,
bigger than the half circle)

[arc ADB] = [circle] - [arc AB].

So m[arc ADB] = 360 - m[arc AB].

The central angle of [arc AB], ∠[brown],
is 60º.

So m[arc ADB] = 360 - 60.

360 - 60 = 300

## Example 3

These two blue angles are the vertical angles.

So these two angles are congruent.

So m∠DOE = 60.

Vertical angles

The central angle of [arc DE], ∠DOE,
is 60º.

So m[arc DE] = 60.

## Example 4

∠[blue], ∠[green], and ∠[brown]

m∠[blue] = [60]
m∠[brown] = [45]

So [60] + m∠[green] + [45] = 180.

60 + 45 = 105

Move +105 to the right side.

180 - 105 = 75

So m∠[green] = 75.

The central angle of [arc BC], ∠[green],
is 75º.

So m[arc BC] = 75.