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?

  • A𝐴𝐡 and 𝐢𝐷
  • B𝐴𝐢 and 𝐷𝐡
  • C𝐴𝐡 and 𝐡𝐢
  • D𝐴𝐷 and 𝐡𝐢

Q2:

Find π‘šπ΄π·.

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 𝐢𝐷.

Q5:

The pictured circle has a diameter of length 4 cm. Determine, to the nearest hundredth, the length of π‘π‘Œ.

Q6:

Given that 𝐴𝐡 is a diameter in a circle of center 𝑀 and π‘šο€»π΄πΆο‡βˆΆπ‘šο€Ίπ·π΅ο†=85∢67, determine π‘šπ΄πΆπ·.

Q7:

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

Q8:

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

Q9:

Find the value of π‘₯, given that π‘šο€»π΄π·ο‡=34∘.

Q10:

Given that 𝐴𝐡 is a diameter in circle 𝑀 and π‘šβˆ π·π‘€π΅=(5π‘₯+12)∘, determine π‘šπ΄πΆ.

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