1. 10.2 Angles and Arcs What you’ll learn: 1.To recognize major arcs, minor arcs, semicircles, and central angles and their measures. 2.To find arc length.

2. Central angles Central angle – an angle whose vertex is at the center of a circle with sides that are radii of the circle. Sum of central angles – the sum of the measures of the central angles of a circle with no interior points in common is 360.  1+  2+  3=360 1 2 3

3. Arcs Arcs are created by central angles. An arc is a piece of a circle. Their measure is directly related to the measure of the central angle that creates the arc. Symbol Three kinds of arcs: Minor arc – measure is less than 180 degrees. Named by 2 letters that are the endpoints. Major arc – measure is more than 180 degrees Named by 3 letters where the 1 st and 3 rd letters are the endpoints of the arc. Semicircle – measure is 180 degress. Named by 3 letters where the 1 st and 3 rd letters are the endpoints of the arc. A B C D E

4. Theorems/Postulates Theorem 10.1 In the same or in congruent circles, two arcs are congruent iff their corresponding central angles are congruent. if  ADB  BDC and vice-versa. Postulate 10.1 Arc Addition Postulate The measure of an arc formed by 2 adjacent arcs is the sum of the measures of the 2 arcs.  WZX+  XZY=  WZY A B C D W X Y Z

5. RV is a diameter of T. a.Find m  RTS b.Find m  QTR Q R S T U V 20x  (5x+5)  (13x-3)  (8x-4) 

6. In P, m  NPM=46, PL bisects  KPM, and OP  KN. Find each measure. 1. 2. 3. K L M N P J O

7. Arc Length Arc length is the actual measure of an arc. It is a fractional part of the circumference. You must know 2 things in order to find arc length: the radius (or diameter) and the arc measure (in degrees). Use the following formula to find arc length ( ) where A=arc measure or Example: Find A BC 7 in 72 

8. Homework p. 533 14-42 even