Lesson Worksheet: Central Angles and Arcs Mathematics • 11th Grade

In this worksheet, we will practice identifying central angles, using their measures to find measures of arcs, identifying adjacent arcs, finding arc lengths, and identifying congruent arcs in congruent circles.

Q1:

Which of the following arcs are adjacent in the given circle?

  • A𝐴𝐵 and 𝐶𝐷
  • B𝐴𝐶 and 𝐷𝐵
  • C𝐴𝐵 and 𝐵𝐶
  • D𝐴𝐷 and 𝐵𝐶

Q2:

Find 𝑚𝐴𝐷.

Q3:

Find the measure of the arc that represents 16 of the circumference of a circle.

Q4:

Consider the given circle. Find the measure of 𝐶𝐷.

Q5:

The pictured circle has a diameter of length 4 cm. Determine, to the nearest hundredth, the length of 𝑍𝑌.

Q6:

Given that 𝐴𝐵 is a diameter in a circle of center 𝑀 and 𝑚𝐴𝐶𝑚𝐷𝐵=8567, determine 𝑚𝐴𝐶𝐷.

Q7:

Consider a circle 𝑀 with two arcs, 𝐴𝐵 and 𝐶𝐷, that have equal measures. 𝐴𝐵 has a length of 5 cm. What is the length of 𝐶𝐷?

Q8:

Consider circle 𝑀 with two chords of equal length, 𝐴𝐷 and 𝐵𝐶. If 𝐴𝐷 has a length of 5 cm. What is the length of 𝐵𝐶?

Q9:

Find the value of 𝑥, given that 𝑚𝐴𝐷=34.

Q10:

Given that 𝐴𝐵 is a diameter in circle 𝑀 and 𝑚𝐷𝑀𝐵=(5𝑥+12), determine 𝑚𝐴𝐶.

Practice Means Progress

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