Worksheet: Measures of Arcs

In this worksheet, we will practice finding measures of arcs based on the measures of central and inscribed angles.

Q1:

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

Q2:

Which of these is equal to the measure of an arc?

  • Athe measure of the central angle subtended by that arc
  • Bthe inscribed angle subtended by that arc

Q3:

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

Q4:

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

Q5:

An arc measures 53120 of the circumference of a circle. What angle does the arc subtend at the center?

Q6:

Suppose that 𝑚∠𝐵𝑀𝐸=84∘. Determine 𝑚∠𝐷.

Q7:

What is 𝑥?

Q8:

Find 𝑚∠𝐴𝐶𝐷 and 𝑚∠𝐵𝐴𝐶.

  • A𝑚∠𝐴𝐶𝐷=67∘, 𝑚∠𝐵𝐴𝐶=67∘
  • B𝑚∠𝐴𝐶𝐷=33.5∘, 𝑚∠𝐵𝐴𝐶=23∘
  • C𝑚∠𝐴𝐶𝐷=67∘, 𝑚∠𝐵𝐴𝐶=23∘
  • D𝑚∠𝐴𝐶𝐷=23∘, 𝑚∠𝐵𝐴𝐶=23∘

Q9:

𝐴 and 𝐵 are two points on a circle center 𝑀 so that the measure of ∠𝐴𝑀𝐵 is 19 of that of its reflex angle. What is the minor arc 𝐴𝐵?

Q10:

Given that 𝑚∠𝐷𝐴𝐵=82∘ and 𝑚𝐴𝐵=50∘, find 𝑚∠𝐴𝐵𝐶.

Q11:

Given that measure arc 𝐴𝐶=87 the measure of arc 𝐵𝐶, find 𝑚∠𝐴.

Q12:

Find 𝑚𝐴𝐶.

Q13:

An arc has a measure of 130∘.

What is the measure of the central angle?

What is the measure of the inscribed angle?

What is the measure of the circumscribed angle?

Q14:

Given that 𝐴𝐵 is a diameter in circle 𝑀 and 𝑚∠𝐷𝑀𝐵=(3𝑥+12)∘, determine 𝑚𝐴𝐶.

Q15:

Given that 𝐴𝐵 is a diameter in circle 𝑀 and 𝑚∠𝐷𝑀𝐵=(3𝑥+12)∘, determine 𝑚𝐴𝐶.

Q16:

Find the measure of the arc that represents 38 of the circumference of a circle.

Q17:

Given that 𝐴𝐵 is a diameter in circle of center 𝑀 and 𝐴𝐶𝐷𝐵=32119, determine 𝑚𝐴𝐶𝐷.

Q18:

Given that 𝐴𝐵 is a diameter in circle of center 𝑀 and 𝐴𝐶𝐷𝐵=914, determine 𝑚𝐴𝐶𝐷.

Q19:

Given that 𝐴𝐵 is a diameter in circle of center 𝑀 and 𝐴𝐶𝐷𝐵=514, determine 𝑚𝐴𝐶𝐷.

Q20:

If 𝑚∠𝐵𝐴𝐶=25∘, what is 𝑚∠𝐹𝐷𝐸?

Q21:

Given that 𝑚∠𝐶𝐵𝐷=116∘, find 𝑥, 𝑦 and 𝑧.

  • A𝑥=32∘, 𝑦=32∘, 𝑧=32∘
  • B𝑥=64∘, 𝑦=64∘, 𝑧=64∘
  • C𝑥=58∘, 𝑦=58∘, 𝑧=58∘
  • D𝑥=61∘, 𝑦=61∘, 𝑧=61∘

Q22:

Find the value of 𝑥.

Q23:

Given that 𝑚∠𝐴𝐵𝐶=30.5∘, find 𝑚∠𝐵𝐷𝐶.

Q24:

In the given figure, which of the following would represent the minor arc passing through 𝐵 and 𝐶?

  • A𝐶𝐵
  • B𝐵𝐶
  • C𝐵𝐶
  • D⃖⃗𝐵𝐶
  • E𝐵𝐶

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