1. Check.4.40 Find angle measures, intercepted arc measures, and segment lengths formed by radii, chords, secants, and tangents intersecting inside and outside circles. Spi.4.8 Solve problems involving area, circumference, area of a sector, and/or arc length of a circle. 10.2 Angles and Arcs

2. "Keep away from people who try to belittle your ambitions. Small people always do that, but the really great make you feel that you, too, can become great." Mark Twain Objective: Find angle measures, arc measures and segment lengths. Solve problems involving angle measures and arc lengths of a circle. The sum of the central angles (angles with vertex at center) of a circle = 360  A E D B C G Major Arc (3 points) Minor Arc (2 points) 60  =60  =360 – 60 = 300  Minor Arc < 180  Major Arc > 180  F H Semi- Circle (3 points) 180  Arc Addition Postulate: The measure of the arc formed by two adjacent arcs is the sum of the measure of the two arcs. In the same or  circles, 2 arcs are  if their central angles are .

3. Measure of Central Angles Find m  AOD and m  AOE m  AOD + m  DOB = 180 m  AOD+ m  DOC+ m  COB=180 25x + 3x + 2x =180 30x = 180 x = 6 m  AOD = 25x = 25(6) = 150 m  AOE = 180 - m  AOD = 180 – 150 = 30

4. Measure of Central Angles Find m  RTS and m  QTR, RV is a Diameter m  RTS+ m  STU + m  UTV = 180 8x -4 +13x – 3+ 5x + 5 =180 26x - 2 = 180 26x = 182 X = 7 m  RTS = 8(7) – 4 = 52 m  QTR = 180- m  QTV =180 - 20(7) = 40

5. Measures of Arcs In circle F, m  DFA = 50 and CF  FB.  BFE   AFD, vertical angles

6. Pie Charts Find the measure of angles for each section. 360  (2%) = 7.2  360  (6%) = 21.6  360  (28%) = 100.8  360  (43%) = 154.8  360  (15%) = 54  360  (4%) = 14.4 

7. Arc Measures In circle P, PR=15, m  QPR = 120. Find the length of QR

8. 10.2 Angles and Arcs Summary Practice Assignment Page 696 12 – 32 even* Honors Page 697 24 - 48 even* Length of an Arc is proportional to measure of the angle and circumference of the circle Minor Arc 180  The sum of the central angles (angles with vertex at center) of a circle = 360  In the same or  circles, 2 arcs are  if their central angles are . Arc Addition Postulate: The measure of the arc formed by two adjacent arcs is the sum of the measure of the two arcs.