Worksheet: Inscribed Angles in a Circle

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In this worksheet, we will practice identifying theorems about inscribed angles, including theorems that state angles subtended by the same arc are equal and the angle subtended by an arc at the center is double the angle subtended at the circumference.

Q1:

Given that 𝑚∠𝐴𝑀𝐷=84∘ and 𝑚∠𝐵𝐶𝐴=(𝑧+14)∘, determine the value of 𝑧.

Q2:

Given that 𝑚∠𝐴𝐵𝐷=44∘, and 𝑚∠𝐶𝐸𝐴=72∘, find 𝑥, 𝑦 and 𝑧.

  • A 𝑥 = 4 4 ∘ , 𝑦 = 6 4 ∘ , 𝑧 = 6 4 ∘
  • B 𝑥 = 6 4 ∘ , 𝑦 = 4 4 ∘ , 𝑧 = 4 4 ∘
  • C 𝑥 = 5 4 ∘ , 𝑦 = 5 4 ∘ , 𝑧 = 4 4 ∘
  • D 𝑥 = 4 4 ∘ , 𝑦 = 5 4 ∘ , 𝑧 = 5 4 ∘

Q3:

From the figure, what is 𝑥?

Q4:

Given that 𝑚∠𝐶𝐵𝐷=116∘, find 𝑥, 𝑦 and 𝑧.

  • A 𝑥 = 5 8 ∘ , 𝑦 = 5 8 ∘ , 𝑧 = 5 8 ∘
  • B 𝑥 = 6 1 ∘ , 𝑦 = 6 1 ∘ , 𝑧 = 6 1 ∘
  • C 𝑥 = 6 4 ∘ , 𝑦 = 6 4 ∘ , 𝑧 = 6 4 ∘
  • D 𝑥 = 3 2 ∘ , 𝑦 = 3 2 ∘ , 𝑧 = 3 2 ∘

Q5:

Find the value of 𝑥.

Q6:

The measure of 𝐷𝐶 is 140∘. Find 𝑚∠𝐸.

Q7:

Given that 𝑚∠𝑀𝐴𝐶=48∘, find 𝐿.

Q8:

Given that 𝑚∠𝐵𝐴𝐶=89∘, find 𝑚∠𝑥.

Q9:

In the given figure, the diameter of circle 𝑀 is 𝐴𝐵. If 𝑚∠𝐴𝐵𝐷=58∘, what is 𝑚∠𝐷𝐸𝐵?

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

Q10:

Given that 𝐴𝐵 is a diameter in the circle 𝑀, and 𝑚∠𝐵𝑀𝐷=59∘, find 𝑚∠𝐴𝐶𝐷 in degrees.

Q11:

Find 𝑚∠𝑍.

Q12:

Given that 𝐵∈𝐷𝐶 and 𝐴𝐵=𝐷𝐵, find 𝑚∠𝐷.

Q13:

Find 𝑚∠𝐵𝐶𝐷 and 𝑚∠𝐵𝐴𝐷.

  • A 𝑚 ∠ 𝐵 𝐶 𝐷 = 6 6 ∘ , 𝑚 ∠ 𝐵 𝐴 𝐷 = 1 1 4 ∘
  • B 𝑚 ∠ 𝐵 𝐶 𝐷 = 1 2 3 ∘ , 𝑚 ∠ 𝐵 𝐴 𝐷 = 5 7 ∘
  • C 𝑚 ∠ 𝐵 𝐶 𝐷 = 5 7 ∘ , 𝑚 ∠ 𝐵 𝐴 𝐷 = 1 2 3 ∘
  • D 𝑚 ∠ 𝐵 𝐶 𝐷 = 1 1 4 ∘ , 𝑚 ∠ 𝐵 𝐴 𝐷 = 6 6 ∘

Q14:

Given that 𝑚∠𝐴𝐵𝐶=30.5∘, find 𝑚∠𝐵𝐷𝐶.

Q15:

Given that 𝑚∠𝐵𝐴𝐷=105∘, find 𝑚∠𝑀𝐵𝐶.

Q16:

Given that 𝐴𝐵 is a diameter of the circle and 𝐷𝐶∥𝐴𝐵, find 𝑚∠𝐴𝐸𝐷.

Q17:

In the figure, 𝑀 is the center of the circle, and ∠𝑀 is the nonreflex angle at 𝑀. Given that 𝑚∠𝑀−𝑚∠𝐴=75∘, find 𝑚∠𝐴.

Q18:

Given that 𝑚∠𝐴=46.5∘, find 𝑥.

Q19:

Given that 𝑚∠𝐴𝐵𝐶=27∘, and 𝑚∠𝐵𝐷𝐴=62∘, find 𝑚∠𝐵𝐷𝐶 and 𝑚∠𝐵𝐶𝐷.

  • A 𝑚 ∠ 𝐵 𝐷 𝐶 = 5 6 ∘ , 𝑚 ∠ 𝐵 𝐶 𝐷 = 8 9 ∘
  • B 𝑚 ∠ 𝐵 𝐷 𝐶 = 8 9 ∘ , 𝑚 ∠ 𝐵 𝐶 𝐷 = 5 6 ∘
  • C 𝑚 ∠ 𝐵 𝐷 𝐶 = 8 9 ∘ , 𝑚 ∠ 𝐵 𝐶 𝐷 = 2 7 ∘
  • D 𝑚 ∠ 𝐵 𝐷 𝐶 = 1 1 2 ∘ , 𝑚 ∠ 𝐵 𝐶 𝐷 = 1 7 8 ∘

Q20:

Find 𝑥.

Q21:

Find 𝑥+𝑦.

Q22:

In the figure, 𝐴𝐸 intersects the circle at 𝐷 and 𝐸, and 𝐴𝐶 intersects the circle at 𝐵 and 𝐶. Given that 𝐴𝐵=𝐵𝐸, find 𝑚∠𝐶𝐷𝐸.

Q23:

If the measure of an arc of a circle is 171∘, what is the measure of the inscribed angle subtended by that arc?

Q24:

Find 𝑚∠𝐴𝐵𝐶.

Q25:

In the figure, 𝑂 is the center and 𝑚∠𝑂𝐴𝐵=59.5∘.

What is the measure of angle 𝐴𝑂𝐵?

What is the measure of angle 𝐴𝐶𝐵?

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