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

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 𝐴𝐡 is a diameter in circle of center 𝑀 and 𝐴𝐢𝐷𝐡=8567, determine π‘šπ΄πΆπ·.

Q5:

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

Q6:

Suppose that π‘šβˆ π΅π‘€πΈ=84∘. Determine π‘šβˆ π·.

Q7:

What is π‘₯?

Q8:

Find π‘šβˆ π΄πΆπ· and π‘šβˆ π΅π΄πΆ.

  • Aπ‘šβˆ π΄πΆπ·=67∘, π‘šβˆ π΅π΄πΆ=67∘
  • Bπ‘šβˆ π΄πΆπ·=33.5∘, π‘šβˆ π΅π΄πΆ=23∘
  • Cπ‘šβˆ π΄πΆπ·=67∘, π‘šβˆ π΅π΄πΆ=23∘
  • Dπ‘šβˆ π΄πΆπ·=23∘, π‘šβˆ π΅π΄πΆ=23∘

Q9:

𝐴 and 𝐡 are two points on a circle center 𝑀 so that the measure of βˆ π΄π‘€π΅ is 19 of that of its reflex angle. What is the minor arc 𝐴𝐡?

Q10:

Given that π‘šβˆ π·π΄π΅=82∘ and π‘šπ΄π΅=50∘, find π‘šβˆ π΄π΅πΆ.

Q11:

Given that measure arc 𝐴𝐢=87 the measure of arc 𝐡𝐢, find π‘šβˆ π΄.

Q12:

Find π‘šπ΄πΆ.

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 𝐴𝐡 is a diameter in circle 𝑀 and π‘šβˆ π·π‘€π΅=(3π‘₯+12)∘, determine π‘šπ΄πΆ.

Q15:

Given that 𝐴𝐡 is a diameter in circle 𝑀 and π‘šβˆ π·π‘€π΅=(3π‘₯+12)∘, determine π‘šπ΄πΆ.

Q16:

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

Q17:

Given that 𝐴𝐡 is a diameter in circle of center 𝑀 and 𝐴𝐢𝐷𝐡=32119, determine π‘šπ΄πΆπ·.

Q18:

Given that 𝐴𝐡 is a diameter in circle of center 𝑀 and 𝐴𝐢𝐷𝐡=914, determine π‘šπ΄πΆπ·.

Q19:

Given that 𝐴𝐡 is a diameter in circle of center 𝑀 and 𝐴𝐢𝐷𝐡=514, determine π‘šπ΄πΆπ·.

Q20:

If π‘šβˆ π΅π΄πΆ=25∘, what is π‘šβˆ πΉπ·πΈ?

Q21:

Given that π‘šβˆ πΆπ΅π·=116∘, find π‘₯, 𝑦 and 𝑧.

  • Aπ‘₯=32∘, 𝑦=32∘, 𝑧=32∘
  • Bπ‘₯=64∘, 𝑦=64∘, 𝑧=64∘
  • Cπ‘₯=58∘, 𝑦=58∘, 𝑧=58∘
  • Dπ‘₯=61∘, 𝑦=61∘, 𝑧=61∘

Q22:

Find the value of π‘₯.

Q23:

Given that π‘šβˆ π΄π΅πΆ=30.5∘, find π‘šβˆ π΅π·πΆ.

Q24:

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

  • Aοƒͺ𝐢𝐡
  • B𝐡𝐢
  • C𝐡𝐢
  • D⃖⃗𝐡𝐢
  • Eοƒͺ𝐡𝐢

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