Central angles and arc measures

Answer Key - Grade 10 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Ari ices a round cookie in three colors. Arcs CD, DF and FC fill circle O in the ratio 2 : 3 : 4. What is the measure of arc DF?

   120
2. 2.

   Bo splits a round flower bed in the park into three parts. Arcs CD, DF and FC fill circle O in the ratio 3 : 5 : 4. What is the measure of arc DF?

   150
3. 3.

   Esme shares a round pizza in three pieces. Arcs CD, DF and FC fill circle O in the ratio 1 : 4 : 3. What is the measure of arc DF?

   180
4. 4.

   Kira draws two hands on a clock face. On circle O, ∠COD = (2x + 4)° and major arc CFD = (3x + 6)°. What is the measure of minor arc CD?

   144
5. 5.

   Milo cuts one wedge from a round cake. On circle O, ∠COD = (3x − 5)° and major arc CFD = (7x + 15)°. What is the measure of minor arc CD?

   100
6. 6.

   Noah paints one wedge on a drum top. On circle O, ∠COD = (4x + 2)° and major arc CFD = (6x + 8)°. What is the measure of minor arc CD?

   142
7. 7.

   Pia asks 40 classmates their favorite snack and shows it in a pie chart; 12 pick popcorn. What central angle, in degrees, does that slice of the pie chart get?

   108
8. 8.

   Ren asks 20 readers their favorite kind of book; 7 pick mysteries. What central angle, in degrees, does that slice of the pie chart get?

   126
9. 9.

   Tala asks 60 students their favorite recess game; 27 pick four square. What central angle, in degrees, does that slice of the pie chart get?

   162
10. 10.

    Zee counts how 80 classmates get to school; 12 ride bikes. What central angle, in degrees, does that slice of the pie chart get?

    54