Worksheet: Inscribed Angles

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In this worksheet, we will practice finding the measure of inscribed angles using the relation between angles and arcs.

Q1:

Given that 𝑚 ∠ 𝐴 𝑀 𝐷 = 8 4 ∘ and 𝑚 ∠ 𝐵 𝐶 𝐴 = ( 𝑧 + 1 4 ) ∘ , determine the value of 𝑧 .

Q2:

Given that 𝑚 ∠ 𝐴 𝐵 𝐷 = 4 4 ∘ , and 𝑚 ∠ 𝐶 𝐸 𝐴 = 7 2 ∘ , find 𝑥 , 𝑦 and 𝑧 .

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

Q3:

From the figure, what is 𝑥 ?

Q4:

Given that 𝑚 ∠ 𝐶 𝐵 𝐷 = 1 1 6 ∘ , find 𝑥 , 𝑦 and 𝑧 .

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

Q5:

Find the value of 𝑥 .

Q6:

The measure of 𝐷 𝐶 is 1 4 0 ∘ . Find 𝑚 ∠ 𝐸 .

Q7:

Given that 𝑚 ∠ 𝑀 𝐴 𝐶 = 4 8 ∘ , find 𝐿 .

Q8:

Given that 𝑚 ∠ 𝐵 𝐴 𝐶 = 8 9 ∘ , find 𝑚 ∠ 𝑥 .

Q9:

In the given figure, the diameter of circle 𝑀 is 𝐴 𝐵 . If 𝑚 ∠ 𝐴 𝐵 𝐷 = 5 8 ∘ , what is 𝑚 ∠ 𝐷 𝐸 𝐵 ?

Q10:

Given that 𝐴 𝐵 is a diameter in the circle 𝑀 , and 𝑚 ∠ 𝐵 𝑀 𝐷 = 5 9 ∘ , find 𝑚 ∠ 𝐴 𝐶 𝐷 in degrees.

Q11:

Find 𝑚 ∠ 𝑍 .

Q12:

Given that 𝐵 ∈ 𝐷 𝐶 and 𝐴 𝐵 = 𝐷 𝐵 , find 𝑚 ∠ 𝐷 .

Q13:

Find 𝑚 ∠ 𝐵 𝐶 𝐷 and 𝑚 ∠ 𝐵 𝐴 𝐷 .

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

Q14:

Given that 𝑚 ∠ 𝐴 𝐵 𝐶 = 3 0 . 5 ∘ , find 𝑚 ∠ 𝐵 𝐷 𝐶 .

Q15:

Given that 𝑚 ∠ 𝐵 𝐴 𝐷 = 1 0 5 ∘ , find 𝑚 ∠ 𝑀 𝐵 𝐶 .

Q16:

Given that 𝐴 𝐵 is a diameter of the circle and 𝐷 𝐶 ⫽ 𝐴 𝐵 , find 𝑚 ∠ 𝐴 𝐸 𝐷 .

Q17:

In the figure, 𝑀 is the centre of the circle, and ∠ 𝑀 is the nonreflex angle at 𝑀 . Given that 𝑚 ∠ 𝑀 − 𝑚 ∠ 𝐴 = 7 5 ∘ , find 𝑚 ∠ 𝐴 .

Q18:

Given that 𝑚 ∠ 𝐴 = 4 6 . 5 ∘ , find 𝑥 .

Q19:

Given that 𝑚 ∠ 𝐴 𝐵 𝐶 = 2 7 ∘ , and 𝑚 ∠ 𝐵 𝐷 𝐴 = 6 2 ∘ , find 𝑚 ∠ 𝐵 𝐷 𝐶 and 𝑚 ∠ 𝐵 𝐶 𝐷 .

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

Q20:

Find 𝑥 .

Q21:

Find 𝑥 + 𝑦 .

Q22:

In the figure, 𝐴 𝐸 intersects the circle at 𝐷 and 𝐸 , and 𝐴 𝐶 intersects the circle at 𝐵 and 𝐶 . Given that 𝐴 𝐵 = 𝐵 𝐸 , find 𝑚 ∠ 𝐶 𝐷 𝐸 .

Q23:

If the measure of an arc of a circle is 1 7 1 ∘ , what is the measure of the inscribed angle subtended by that arc?

Q24:

Find 𝑚 ∠ 𝐴 𝐵 𝐶 .

Q25:

In the figure, is the centre and .

What is the size of angle ?

  • A
  • B
  • C
  • D
  • E

What is the size of angle ?

  • A
  • B
  • C
  • D
  • E

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