Worksheet: The Sum of Central Angles

In this worksheet, we will practice identifying central angles and finding their measures using their portion of the circle and their sum.

Q1:

In the given figure, the circle has center 𝑀 and radius 7 cm. Given that 𝐴 𝐵 = 1 4 . 9 c m , find 𝑀 𝐵 , rounded to the nearest tenth, and 𝑚 𝐴 𝑀 𝐶 .

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

Q2:

How many 1 angles are in a circle?

Q3:

How many turns are needed to make a complete turn?

  • A6
  • B5
  • C8
  • D4
  • E3

Q4:

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

  • A12
  • B10
  • C15
  • D8
  • E9

Q5:

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

  • A 1 5 0
  • B 2 7 0
  • C 1 8 0
  • D 1 2 0
  • E 9 0

Q6:

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

  • A
  • B
  • C
  • D
  • E

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 𝐴 𝑀 𝐵 .

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 𝑀 𝐷 and 𝐴 𝐵 and we have 𝑀 𝐶 𝐴 𝐵 and 𝑀 𝐶 = 4 2 c m . Find the central angle of the major circular segment 𝐴 𝐹 𝐵 giving the answer to the nearest second.

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

Q10:

A circle has a circumference of 1 6 𝜋 units. Find, in degrees, the measure of the central angle of an arc with a length of 3 𝜋 units.

Q11:

In the figure, given that the circumference is 96 and 𝐴 𝐵 = 1 2 , find 𝜃 .

Q12:

What is the size of half a circle?

  • A
  • B
  • C
  • D
  • E

Q13:

Circle 𝑀 has radius 32 and 𝐴 𝐵 = 5 6 . 5 . Determine 𝑚 𝐷 𝑀 𝑋 and 𝐷 𝐸 to the nearest hundredth.

  • A 1 4 4 , 28.25
  • B 5 4 , 15.03
  • C 1 0 8 , 56.50
  • D 1 2 6 , 16.97

Q14:

In the given figure, the circle has center 𝑀 and radius 9.9 cm. Given that 𝐴 𝐵 = 1 7 . 1 c m , find 𝑀 𝐵 , rounded to the nearest tenth, and 𝑚 𝐴 𝑀 𝐶 .

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

Q15:

In the given figure, the circle has center 𝑀 and radius 8.5 cm. Given that 𝐴 𝐵 = 1 6 . 5 c m , find 𝑀 𝐵 , rounded to the nearest tenth, and 𝑚 𝐴 𝑀 𝐶 .

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

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