Worksheet: Inscribed Angles in a Circle

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 𝑚𝐴𝑀𝐷=84 and 𝑚𝐵𝐶𝐴=(𝑧+14), determine the value of 𝑧.

Q2:

Given that 𝑚𝐴𝐵𝐷=44, and 𝑚𝐶𝐸𝐴=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 𝑚𝐶𝐵𝐷=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 𝑚𝐸.

Q7:

Given that 𝑚𝑀𝐴𝐶=48, find 𝐿.

Q8:

Given that 𝑚𝐵𝐴𝐶=89, find 𝑚𝑥.

Q9:

In the given figure, the diameter of circle 𝑀 is 𝐴𝐵. If 𝑚𝐴𝐵𝐷=58, what is 𝑚𝐷𝐸𝐵?

  • 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 𝑚𝐵𝑀𝐷=59, find 𝑚𝐴𝐶𝐷 in degrees.

Q11:

Find 𝑚𝑍.

Q12:

Given that 𝐵𝐷𝐶 and 𝐴𝐵=𝐷𝐵, find 𝑚𝐷.

Q13:

Find 𝑚𝐵𝐶𝐷 and 𝑚𝐵𝐴𝐷.

  • 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 𝑚𝐴𝐵𝐶=30.5, find 𝑚𝐵𝐷𝐶.

Q15:

Given that 𝑚𝐵𝐴𝐷=105, find 𝑚𝑀𝐵𝐶.

Q16:

Given that 𝐴𝐵 is a diameter of the circle and 𝐷𝐶𝐴𝐵, find 𝑚𝐴𝐸𝐷.

Q17:

In the figure, 𝑀 is the center of the circle, and 𝑀 is the nonreflex angle at 𝑀. Given that 𝑚𝑀𝑚𝐴=75, find 𝑚𝐴.

Q18:

Given that 𝑚𝐴=46.5, find 𝑥.

Q19:

Given that 𝑚𝐴𝐵𝐶=27, and 𝑚𝐵𝐷𝐴=62, find 𝑚𝐵𝐷𝐶 and 𝑚𝐵𝐶𝐷.

  • 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 𝑚𝐶𝐷𝐸.

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 𝑚𝐴𝐵𝐶.

Q25:

In the figure, 𝑂 is the center and 𝑚𝑂𝐴𝐵=59.5.

What is the measure of angle 𝐴𝑂𝐵?

What is the measure of angle 𝐴𝐶𝐵?

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