Problem 2 Finding the Measures of Arcs

What is the measure of each arc in ⊙ circle dot   O?

1. B C ⌢ m B C ⌢ = m ∠ B O C = 32 modified b c with frown above , m , modified b c with frown above , equals m angle b o c equals 32
2. B D ⌢ m B D ⌢ = m B C ⌢ + m C D ⌢   m B D ⌢ = 32 + 58 = 90 table with 2 rows and 2 columns , row1 column 1 , modified b d with frown above , column 2 m , modified b d with frown above , equals m , modified b c with frown above , plus m , modified c d with frown above , row2 column 1 , , column 2 m , modified b d with frown above , equals 32 plus 58 equals 90 , end table
3. A B C ⌢ A B C ⌢  is a semicircle.   m A B C ⌢ = 180 table with 2 rows and 2 columns , row1 column 1 , modified eh b c with frown above , column 2 modified eh b c with frown above . is a semicircle. , row2 column 1 , , column 2 m . modified eh b c with frown above . equals 180 , end table
4. A B ⌢ m A B ⌢ = 180 − 32 = 148 modified eh b with frown above , m , modified eh b with frown above , equals 180 minus 32 equals 148

✓ Got It?

2. What is the measure of each arc in ⊙ C ? circle dot c question mark
   1. m P R ⌢ m , modified p r with frown above
   2. m R S ⌢ m , modified r s with frown above
   3. m P R Q ⌢ m . modified p r q with frown above
   4. m P Q R ⌢ m . modified p q r with frown above

Take note Theorem 10-9: Circumference of a Circle

The circumference of a circle is π pi  times the diameter.

C = π d c equals , pi d  or C = 2 π r c equals 2 . pi r