1. Circles: Central Angles & Arc Measure
Tutorial 8b

2. 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
Central Angle =
 APB P
Semicircle =
CDB D
“ ” is a symbol for arc.

3. 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
Minor arcs below are:
AB or AC A
The measure of arc AB is equal to the measure of APB. This can be written using the following symbols:
135º C B P D
mAB = 135º

4. 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
Major arc =
ACB or BDA C B P D

5. Central Angles and Arcs
Adjacent arcs are two arcs in the same circle that have exactly one point in common. A
Circle P
Adjacent arcs:
AC & AB or
AB & BD C B P D

6. 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
Circle P
85º
mAB + mBD = mAD C B
Example: P
45º
mAB + mBD = mAD D
85º º = 130º
mAD = 130 º

7. 1. 70 20 2. 3.
160 4.
= 270 5.
= 144 6. 36 7.
180 8. 36
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Check answers

8. 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.
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check your answers

9. Potatoes: 8.8% of 360º = 31.68º Green beans: 11.9% of 360º = 42.84º3. 4. 5.
Potatoes: 8.8% of 360º = 31.68º
Green beans: % of 360º = 42.84º
Corn: % of 360º = 54.36º
Carrots: % of 360º = 38.88º
Broccoli: % of 360º = 70.92º

10. The End
Time to move on
to the assignment or
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