Circles: Central Angles
& Arc Measure
Tutorial 8b
Central Angles and Arcs
 A central angle is an angle whose vertex is
at the center of the circle.
 A semicircle is a half circle. The measure of
a semicircle is 180.
A
Circle P
C
B
P
D
Central Angle =  APB
Semicircle = CDB
“
” is a symbol for arc.
Central Angles and Arcs
 A minor arc is shorter than a semicircle.
The measure of a minor arc is the measure
of its corresponding central angle.
Circle P
A
135º
C
P
Minor arcs below are:AB or AC
The measure of arc AB is
equal to the measure of
B
APB. This can be written
using the following symbols:
D
mAB = 135º
Central Angles and Arcs
 A major arc is longer than a semicircle.
The measure of a major arc is the 360 minus
the measure of its related minor arc.
A
Circle P
C
B
P
D
Major arc = ACB or BDA
Central Angles and Arcs
 Adjacent arcs are two arcs in the same
circle that have exactly one point in
common.
A
Circle P
C
B
P
Adjacent arcs: AC & AB or
AB & BD
D
Central Angles and Arcs
 Arc Addition Postulate: The measure of
the arc formed by two adjacent arcs is the
sum of the two arcs.
A
85º
Circle P
mAB + mBD = mAD
C
P
B
Example:
45º mAB + mBD = mAD
D
85º + 45º = 130º
mAD = 130 º
1.
70
2.
3.
160
4.
5.
180 - 36 = 144 6.
7.
180
8.
20
360 - 90 = 270
36
36
Click to
Check answers
1.
2.
3.
4.
5.
Since there are 360º in a circle, simply multiply each percent
by 360 to find the measure of each central angle in the graph.
Click here to
check your answers
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
Potatoes:
Green beans:
Corn:
Carrots:
Broccoli:
8.8% of 360º = 31.68º
11.9% of 360º = 42.84º
15.1% of 360º = 54.36º
10.8% of 360º = 38.88º
19.7% of 360º = 70.92º