1. 10-2 Angles and Arcs

2. Central Angles
Have the center of the circle as the vertex and its sides are 2 radii of the circle
The sum of the measures of the central angles of a circle is 360°
m<1 + m<2 + m<3 + m<4 = 360°
m<1 + m<2 = 180° since the AC is a diameter of the circle B 1 2 A C 4 3 D

3. Example: RV is a diameter of circle T
Find m<RTS
Find m<QTR R S Q
8x-4 T
13x-3
20x
5x+5 U V

4. Arcs The edge of the circle cut off by the radii of the central angle
MINOR ARC – the measure of the minor arc is equal to the measure of the central angle
m AC =110° A
110° C

5. Arcs MAJOR ARC – around the circle on the OUTSIDE of the central angle
Named by 2 endpoints and another point on the circle
Measure is 360° minus the measure of the minor arc
m DFE = 360°-50°=310° D F
50° E

6. Arcs SEMICIRCLE – the arc made by the diameter of the circle
Named by the endpoints and another point on the circle
All semicircle have a measure of 180°
m JML = 180° M J N L

7. Arcs
Arcs with the same measure in the same circle or in congruent circles are congruent
2 Arcs are congruent if their central angles are congruent
Arcs that have exactly one point in common are adjacent arcs
The measures of adjacent arcs can be added

8. Example: PL bisects <KPM and OP┴KN
Find m OK
Find m LM
Find m JKO L K P J M
46° O N

9. Arc Length The length of an arc is proportional to the circumference
Example: Find length of AD
AC = 9
m<ABD = 40 A B C D