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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:

The circle 𝑀 in the figure has radius 7 cm. Given that 𝐴 𝐡 = 1 4 . 9 c m , find π‘š ∠ 𝐴 𝑀 𝐢 and 𝑀 𝐡 rounded to the nearest tenth.

  • A π‘š ∠ 𝐴 𝑀 𝐢 = 1 1 9 ∘ , 𝑀 𝐡 = 1 6 . 5 c m
  • B π‘š ∠ 𝐴 𝑀 𝐢 = 1 5 1 ∘ , 𝑀 𝐡 = 1 6 . 5 c m
  • C π‘š ∠ 𝐴 𝑀 𝐢 = 1 5 1 ∘ , 𝑀 𝐡 = 1 4 . 9 c m
  • D π‘š ∠ 𝐴 𝑀 𝐢 = 1 1 9 ∘ , 𝑀 𝐡 = 1 3 . 2 c m

Q2:

The circle 𝑀 in the figure has radius 9.9 cm. Given that 𝐴 𝐡 = 1 7 . 1 c m , find π‘š ∠ 𝐴 𝑀 𝐢 and 𝑀 𝐡 rounded to the nearest tenth.

  • A π‘š ∠ 𝐴 𝑀 𝐢 = 1 6 6 ∘ , 𝑀 𝐡 = 1 9 . 8 c m
  • B π‘š ∠ 𝐴 𝑀 𝐢 = 1 0 4 ∘ , 𝑀 𝐡 = 1 9 . 8 c m
  • C π‘š ∠ 𝐴 𝑀 𝐢 = 1 0 4 ∘ , 𝑀 𝐡 = 1 7 . 1 c m
  • D π‘š ∠ 𝐴 𝑀 𝐢 = 1 6 6 ∘ , 𝑀 𝐡 = 1 3 . 9 c m

Q3:

The circle 𝑀 in the figure has radius 8.5 cm. Given that 𝐴 𝐡 = 1 6 . 5 c m , find π‘š ∠ 𝐴 𝑀 𝐢 and 𝑀 𝐡 rounded to the nearest tenth.

  • A π‘š ∠ 𝐴 𝑀 𝐢 = 1 3 7 ∘ , 𝑀 𝐡 = 1 8 . 6 c m
  • B π‘š ∠ 𝐴 𝑀 𝐢 = 1 3 3 ∘ , 𝑀 𝐡 = 1 8 . 6 c m
  • C π‘š ∠ 𝐴 𝑀 𝐢 = 1 3 3 ∘ , 𝑀 𝐡 = 1 6 . 5 c m
  • D π‘š ∠ 𝐴 𝑀 𝐢 = 1 3 7 ∘ , 𝑀 𝐡 = 1 4 . 1 c m

Q4:

Find π‘š ∠ 𝐴 𝑀 𝐡 .

  • A 3 0 6 ∘
  • B 2 7 ∘
  • C 7 6 ∘
  • D 1 2 6 ∘

Q5:

𝑀 is a circle with radius 54 cm, 𝑀 𝐢 βŸ‚ 𝐴 𝐡 and 𝑀 𝐢 = 4 2 c m . Find the central angle of the major circular segment 𝐴 𝐹 𝐡 giving the answer to the nearest second.

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

Q6:

How many 1 ∘ angles are in a circle?

Q7:

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

Q8:

Circle 𝑀 has radius 32 and 𝐴 𝐡 = 5 6 . 5 . Determine π‘š ∠ 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

Q9:

How many 4 5 ∘ angles does it take to make a full turn?

Q10:

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

Q11:

In the figure, given that the circumference is 96 and 𝐴 𝐡 = 1 2 , find πœƒ .

Q12:

What is the measure of half a circle?

Q13:

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

Q14:

How many 9 0 ∘ turns are needed to make a complete turn?

Q15:

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

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