are diameters. Find the indicated measures. 1) 2) 3) 4)

Warm-up 50 A B C M N P 1. Let AM = 8, BP = 7, and CA = 18. Find the perimeter of the triangle. 24 A B C 2. Find ACB 3. MCY = 270 Find BC. 20 M B Y C

1) B2) 58° 3) 140°4) 46° 5) 63°6) 28° 7) 123°8) 90° 9) 42°10) 58° 11) 48°12) 58° 13) 42°14) 96° 15) 180°16) x = 14, y = 38 17) x = 58, y = 2918) x = 72, y = 90

Math II UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MM2G1, MM2G2 Today’s Question: What other angle relationships do we know for circles? Standard: MM2G3.b

6.5 Other Angles in a Circle

Case I: Vertex is ON the circle ANGLE ARC ANGLE ARC

Ex. 1 Find m  1. A B C 124° 1 m  1 = 62 

Ex. 2 Find m  1. 84° 1 m  1 = 42 

Ex. 3 Find m  ° 1 m  1 = 79 

Case II: Vertex is inside the circle A B C D ANGLE ARC

Ex. 4 Find m  1. A B C D 1 93° 113° m  1 = 103 

Ex. 5 Find mQT. N Q T M 92  84  mQT = 100 

Homework: Workbook p. 225 #1-9 p. 226 #17-19

Case III: Vertex is outside the circle A B C D ANGLE LARGE ARC small ARC ANGLE LARGE ARC small ARC LARGE ARC ANGLE

A B D 1 Ex. 6 Find m  1. 65° 15° m<1 = 25 degrees

A B Ex. 7 Find mAB. 27° 70° mAB = 16 degrees

1 Ex. 8 Find m  ° m<1 = 80 degrees

Classwork Workbook p. 225 #10-16; p. 227 #20, 21 Homework: Textbook p. 208 #19, 20; p. 214 #1-12