Worksheet: Inscribed Angles

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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