Worksheet: Central Angles in a Circle

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 𝑚𝐴𝑀𝐶.

  • A 𝑀 𝐵 = 1 4 . 9 c m , 𝑚 𝐴 𝑀 𝐶 = 1 5 1
  • B 𝑀 𝐵 = 1 6 . 5 c m , 𝑚 𝐴 𝑀 𝐶 = 1 1 9
  • C 𝑀 𝐵 = 1 3 . 2 c m , 𝑚 𝐴 𝑀 𝐶 = 1 1 9
  • D 𝑀 𝐵 = 1 6 . 5 c m , 𝑚 𝐴 𝑀 𝐶 = 1 5 1

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:

Jacob 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 𝑚𝐴𝑀𝐵.

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 𝑀𝐶𝐴𝐵 and 𝑀𝐶=42cm. Find the central angle of the major circular segment 𝐴𝐹𝐵 giving the answer to the nearest second.

  • A 2 8 4 1 5
  • B 2 8 2 6 5 4
  • C 3 2 2 7 3 0
  • D 3 2 1 3 2 7

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 𝑚𝐷𝑀𝑋 and 𝐷𝐸 to the nearest hundredth.

  • A 1 0 8 , 56.50
  • B 1 4 4 , 28.25
  • C 1 2 6 , 16.97
  • D 5 4 , 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 𝑚𝐴𝑀𝐶.

  • A 𝑀 𝐵 = 1 7 . 1 c m , 𝑚 𝐴 𝑀 𝐶 = 1 0 4
  • B 𝑀 𝐵 = 1 9 . 8 c m , 𝑚 𝐴 𝑀 𝐶 = 1 6 6
  • C 𝑀 𝐵 = 1 3 . 9 c m , 𝑚 𝐴 𝑀 𝐶 = 1 6 6
  • D 𝑀 𝐵 = 1 9 . 8 c m , 𝑚 𝐴 𝑀 𝐶 = 1 0 4

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 𝑚𝐴𝑀𝐶.

  • A 𝑀 𝐵 = 1 6 . 5 c m , 𝑚 𝐴 𝑀 𝐶 = 1 3 3
  • B 𝑀 𝐵 = 1 8 . 6 c m , 𝑚 𝐴 𝑀 𝐶 = 1 3 7
  • C 𝑀 𝐵 = 1 4 . 1 c m , 𝑚 𝐴 𝑀 𝐶 = 1 3 7
  • D 𝑀 𝐵 = 1 8 . 6 c m , 𝑚 𝐴 𝑀 𝐶 = 1 3 3

Q16:

The given figure shows a circle with center 𝑂.

Which of the following is a central angle?

  • A 𝐵 𝐴 𝐶
  • B 𝐶 𝐷 𝐵
  • C 𝑂 𝐶 𝐷
  • D 𝐵 𝑂 𝐶
  • E 𝐵 𝐷 𝐶

Which of the following is an inscribed angle?

  • A 𝐵 𝐴 𝐶
  • B 𝑂 𝐶 𝐷
  • C 𝐵 𝐷 𝐶
  • D 𝐶 𝐷 𝐵
  • E 𝐵 𝑂 𝐶

Which of the following is a circumscribed angle?

  • A 𝐵 𝑂 𝐶
  • B 𝑂 𝐶 𝐷
  • C 𝐵 𝐴 𝐶
  • D 𝐵 𝑂 𝐶
  • E 𝐵 𝐷 𝐶

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