Measure of an Arc

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.

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

Example 1

Find the measure of arc AB. The measure of angle AB = 60. The measure of angle CD = 45.

m[arc AB] = m∠(blue) = 60

Just like this arc,
if 0 < m[arc] < 180,
then it's called the minor arc.

Example 2

Find the measure of arc ADB. The measure of angle AB = 60. The measure of angle CD = 45.

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

Find the measure of arc DE. The measure of angle AB = 60. The measure of angle CD = 45.

The blue angles are congruent.

Vertical angles

So m[arc DE] = m∠(blue) = 60.

Example 4

Find the measure of arc BC. The measure of angle AB = 60. The measure of angle CD = 45.

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

60 + m[arc BC] + 45 = 180