Measure of an Arc
How to find the measure of an arc: definition, examples, and their solutions.
The measure of an arc
is the measure of the arc's central angle.
The central angle of [arc AB], ∠AOB,
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)
[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],
So m[arc ADB] = 360 - 60.
360 - 60 = 300
So m[arc ADB] = 300.
These two blue angles are the vertical angles.
So these two angles are congruent.
So m∠DOE = 60.
The central angle of [arc DE], ∠DOE,
So m[arc DE] = 60.
∠[blue], ∠[green], and ∠[brown]
form a line: AD.
m∠[blue] = 
m∠[brown] = 
So  + m∠[green] +  = 180.
60 + 45 = 105
Move +105 to the right side.
180 - 105 = 75
So m∠[green] = 75.
The central angle of [arc BC], ∠[green],
So m[arc BC] = 75.