Worksheet: Central Angles in a Circle

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In this worksheet, we will practice identifying a central angle in a circle and finding its measure using its properties.

Q1:

In the given figure, the circle has center 𝑀and radius 7 cm. Given that 𝐴𝐵=14.9cm, find 𝑀𝐵, rounded to the nearest tenth, and 𝑚∠𝐴𝑀𝐶.

  • A𝑀𝐵=14.9cm, 𝑚∠𝐴𝑀𝐶=151∘
  • B𝑀𝐵=16.5cm, 𝑚∠𝐴𝑀𝐶=119∘
  • C𝑀𝐵=13.2cm, 𝑚∠𝐴𝑀𝐶=119∘
  • D𝑀𝐵=16.5cm, 𝑚∠𝐴𝑀𝐶=151∘

Q2:

How many 1 ∘ angles are in a circle?

Q3:

How many 90∘ turns are needed to make a complete turn?

Q4:

How many 45∘ angles does it take to make a full turn?

Q5:

Jackson turns one-third of a full turn. How many degrees is this?

Q6:

This circle is divided into 3 equal parts. What is the angle of each part?

Q7:

What is the value of the central angle of a circular sector when a circular segment and a circular sector have the same area?

Q8:

Find 𝑚∠𝐴𝑀𝐵.

Q9:

𝐴, 𝐵, and 𝐷 are three points on a circle with radius 54 cm and center 𝑀. The point 𝐶 is the intersection of 𝑀𝐷 and 𝐴𝐵 and we have 𝑀𝐶⟂𝐴𝐵 and 𝑀𝐶=42cm. Find the central angle of the major circular segment 𝐴𝐹𝐵 giving the answer to the nearest second.

  • A28415′∘
  • B2826′54′′∘
  • C3227′30′′∘
  • D3213′27′′∘

Q10:

A circle has a circumference of 16𝜋 units. Find, in degrees, the measure of the central angle of an arc with a length of 3𝜋 units.

Q11:

In the figure, given that the circumference is 96 and 𝐴𝐵=12, find 𝜃.

Q12:

What is the measure of half a circle?

Q13:

Circle 𝑀 has radius 32 and 𝐴𝐵=56.5. Determine 𝑚∠𝐷𝑀𝑋 and 𝐷𝐸 to the nearest hundredth.

  • A108∘, 56.50
  • B144∘, 28.25
  • C126∘, 16.97
  • D54∘, 15.03

Q14:

In the given figure, the circle has center 𝑀and radius 9.9 cm. Given that 𝐴𝐵=17.1cm, find 𝑀𝐵, rounded to the nearest tenth, and 𝑚∠𝐴𝑀𝐶.

  • A𝑀𝐵=17.1cm, 𝑚∠𝐴𝑀𝐶=104∘
  • B𝑀𝐵=19.8cm, 𝑚∠𝐴𝑀𝐶=166∘
  • C𝑀𝐵=13.9cm, 𝑚∠𝐴𝑀𝐶=166∘
  • D𝑀𝐵=19.8cm, 𝑚∠𝐴𝑀𝐶=104∘

Q15:

In the given figure, the circle has center 𝑀and radius 8.5 cm. Given that 𝐴𝐵=16.5cm, find 𝑀𝐵, rounded to the nearest tenth, and 𝑚∠𝐴𝑀𝐶.

  • A𝑀𝐵=16.5cm, 𝑚∠𝐴𝑀𝐶=133∘
  • B𝑀𝐵=18.6cm, 𝑚∠𝐴𝑀𝐶=137∘
  • C𝑀𝐵=14.1cm, 𝑚∠𝐴𝑀𝐶=137∘
  • D𝑀𝐵=18.6cm, 𝑚∠𝐴𝑀𝐶=133∘

Q16:

The given figure shows a circle with center 𝑂.

Which of the following is a central angle?

  • A∠𝐵𝐴𝐶
  • B∠𝐶𝐷𝐵
  • C∠𝑂𝐶𝐷
  • D∠𝐵𝑂𝐶
  • E∠𝐵𝐷𝐶

Which of the following is an inscribed angle?

  • A∠𝐵𝐴𝐶
  • B∠𝑂𝐶𝐷
  • C∠𝐵𝐷𝐶
  • D∠𝐶𝐷𝐵
  • E∠𝐵𝑂𝐶

Which of the following is a circumscribed angle?

  • A∠𝐵𝑂𝐶
  • B∠𝑂𝐶𝐷
  • C∠𝐵𝐴𝐶
  • D∠𝐵𝑂𝐶
  • E∠𝐵𝐷𝐶

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