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Lesson: The Sum of Central Angles

Sample Question Videos

Worksheet • 15 Questions • 1 Video

Q1:

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

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

Q2:

How many 1 ∘ angles are in a circle?

Q3:

How many turns are needed to make a complete turn?

  • A4
  • B3
  • C5
  • D8
  • E6

Q4:

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

  • A8
  • B9
  • C10
  • D15
  • E12

Q5:

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

  • A 1 2 0 ∘
  • B 9 0 ∘
  • C 2 7 0 ∘
  • D 1 8 0 ∘
  • E 1 5 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 π‘š ∠ 𝐴 𝑀 𝐡 .

Q9:

𝐴 , 𝐡 , and 𝐷 are three points on a circle with radius 54 cm and center 𝑀 . The point 𝐢 is the intersection of 𝑀 𝐷 and 𝐴 𝐡 and we have 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 2 8 2 6 β€² 5 4 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 3 2 2 7 β€² 3 0 β€² β€² ∘

Q10:

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.

Q11:

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

Q12:

What is the size of half a circle?

  • A
  • B
  • C
  • D
  • E

Q13:

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

Q14:

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

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

Q15:

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

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