Central angles and arc measures

Answer Key - Grade 10 Math Worksheet

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

1. 1.

   Ari builds a spinner with four slices. Points C, D, F and G sit in order on circle O. What is the measure of arc DCG, in degrees?

   170
2. 2.

   Bo marks four points on a round clock face. Points C, D, F and G sit in order on circle O. What is the measure of arc DCG, in degrees?

   205
3. 3.

   Esme cuts a round pizza into four unequal slices. Points C, D, F and G sit in order on circle O. What is the measure of arc DCG, in degrees?

   155
4. 4.

   Jun plans four paths from the center of a round park. Points C, D, F and G sit in order on circle O. What is the measure of arc DCG, in degrees?

   220
5. 5.

   Kira designs a spinner with three slices. Around center O, ∠COD = (2x + 10)°, ∠DOF = (3x + 20)° and ∠FOC = 130°. What is x?

   40
6. 6.

   Luz cuts a round pizza into three pieces. Around center O, ∠COD = (x + 30)°, ∠DOF = (4x − 10)° and ∠FOC = 150°. What is x?

   38
7. 7.

   Milo plans a round rug made of three wedges. Around center O, ∠COD = (3x)°, ∠DOF = (2x + 15)° and ∠FOC = 95°. What is x?

   50
8. 8.

   Noah paints three wedges on a round clock face. Around center O, ∠COD = (3x − 6)°, ∠DOF = (2x + 12)° and ∠FOC = 104°. What is x?

   50
9. 9.

   Pia cuts a pizza in half, then cuts one half into two pieces. CD is a diameter of circle O; ∠COF = (3x + 5)° and ∠FOD = (2x + 15)°. What is x?

   32
10. 10.

    Ren draws a line through the center of a clock, then a hand. CD is a diameter of circle O; ∠COF = (x + 40)° and ∠FOD = (3x)°. What is x?

    35