# 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

So m[arc *ADB*] = 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]

form a line: *AD*.

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.