Worksheet: Arcs and Arcs Measures

In this worksheet, we will practice finding measures of arcs.

Q1:

Given that 𝐴 𝐡 is a diameter in circle 𝑀 and π‘š ∠ 𝐷 𝑀 𝐡 = ( 5 π‘₯ + 1 2 ) ∘ , determine π‘š 𝐴 𝐢 .

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 1 6 of the circumference of a circle.

Q4:

Given that 𝐴 𝐡 is a diameter in circle of center 𝑀 and 𝐴 𝐢 𝐷 𝐡 = 8 5 6 7 , determine π‘š 𝐴 𝐢 𝐷 .

Q5:

An arc measures 5 3 1 2 0 of the circumference of a circle. What angle does the arc subtend at the centre?

  • A 4 0 ∘
  • B 8 0 ∘
  • C 3 1 8 ∘
  • D 1 5 9 ∘

Q6:

Suppose that π‘š ∠ 𝐡 𝑀 𝐸 = 8 4 ∘ . Determine π‘š ∠ 𝐷 .

Q7:

What is π‘₯ ?

Q8:

Find π‘š ∠ 𝐴 𝐢 𝐷 and π‘š ∠ 𝐡 𝐴 𝐢 .

  • A π‘š ∠ 𝐴 𝐢 𝐷 = 2 3 ∘ , π‘š ∠ 𝐡 𝐴 𝐢 = 2 3 ∘
  • B π‘š ∠ 𝐴 𝐢 𝐷 = 6 7 ∘ , π‘š ∠ 𝐡 𝐴 𝐢 = 6 7 ∘
  • C π‘š ∠ 𝐴 𝐢 𝐷 = 6 7 ∘ , π‘š ∠ 𝐡 𝐴 𝐢 = 2 3 ∘
  • D π‘š ∠ 𝐴 𝐢 𝐷 = 3 3 . 5 ∘ , π‘š ∠ 𝐡 𝐴 𝐢 = 2 3 ∘

Q9:

𝐴 and 𝐡 are two points on a circle center 𝑀 so that the measure of ∠ 𝐴 𝑀 𝐡 is 1 9 of that of its reflex angle. What is the minor arc 𝐴 𝐡 ?

Q10:

Given that π‘š ∠ 𝐷 𝐴 𝐡 = 8 2 ∘ and π‘š 𝐴 𝐡 = 5 0 ∘ , find π‘š ∠ 𝐴 𝐡 𝐢 .

Q11:

Given that measure arc 𝐴 𝐢 = 8 7 the measure of arc 𝐡 𝐢 , find π‘š ∠ 𝐴 .

Q12:

Find π‘š 𝐴 𝐢 .

Q13:

An arc has a measure of 1 3 0 ∘ .

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 𝐴 𝐡 is a diameter in circle 𝑀 and π‘š ∠ 𝐷 𝑀 𝐡 = ( 3 π‘₯ + 1 2 ) ∘ , determine π‘š 𝐴 𝐢 .

Q15:

Given that 𝐴 𝐡 is a diameter in circle 𝑀 and π‘š ∠ 𝐷 𝑀 𝐡 = ( 3 π‘₯ + 1 2 ) ∘ , determine π‘š 𝐴 𝐢 .

Q16:

Find the measure of the arc that represents 3 8 of the circumference of a circle.

Q17:

Given that 𝐴 𝐡 is a diameter in circle of center 𝑀 and 𝐴 𝐢 𝐷 𝐡 = 3 2 1 1 9 , determine π‘š 𝐴 𝐢 𝐷 .

Q18:

Given that 𝐴 𝐡 is a diameter in circle of center 𝑀 and 𝐴 𝐢 𝐷 𝐡 = 9 1 4 , determine π‘š 𝐴 𝐢 𝐷 .

Q19:

Given that 𝐴 𝐡 is a diameter in circle of center 𝑀 and 𝐴 𝐢 𝐷 𝐡 = 5 1 4 , determine π‘š 𝐴 𝐢 𝐷 .

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