10 2 Angles and Arcs What youll learn

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.

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 1+ 2+ 3=360 2 3

Arcs are created by central angles. An arc is a piece of a circle. Their measure is directly related to the measure B of the central angle that creates the arc. E Symbol C A Three kinds of arcs: Minor arc – measure is less than 180 degrees. D 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.

Theorems/Postulates Theorem 10. 1 In the same or in congruent circles, two arcs are congruent iff their corresponding central A angles are congruent. D if ADB BDC and B vice-versa. C Postulate 10. 1 Arc Addition Postulate The measure of an arc formed by 2 adjacent arcs is W the sum of the measures of the 2 arcs. X WZX+ XZY= WZY Z Y

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

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

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 A or Example: Find 72 C 7 in B

Homework p. 533 14 -42 even