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Worksheet: Finding the Measure of an Inscribed Angle in a Circle

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

Q1:

Given that π‘š ∠ 𝐴 𝑀 𝐷 = 8 4 ∘ and π‘š ∠ 𝐡 𝐢 𝐴 = ( 𝑧 + 1 4 ) ∘ , determine the value of 𝑧 .

Q2:

From the figure, what is π‘₯ ?

Q3:

Given that π‘š ∠ 𝐢 𝐡 𝐷 = 1 1 6 ∘ , find π‘₯ , 𝑦 and 𝑧 .

  • A π‘₯ = 6 1 ∘ , 𝑦 = 6 1 ∘ , 𝑧 = 6 1 ∘
  • B π‘₯ = 6 4 ∘ , 𝑦 = 6 4 ∘ , 𝑧 = 6 4 ∘
  • C π‘₯ = 5 8 ∘ , 𝑦 = 5 8 ∘ , 𝑧 = 5 8 ∘
  • D π‘₯ = 3 2 ∘ , 𝑦 = 3 2 ∘ , 𝑧 = 3 2 ∘

Q4:

Find the value of π‘₯ .

Q5:

Find the value of π‘₯ .

Q6:

The measure of 𝐷 𝐢 is 1 4 0 ∘ . Find π‘š ∠ 𝐸 .

Q7:

Given that , find .

  • A48
  • B228
  • C66
  • D114

Q8:

Given that , find .

  • A
  • B
  • C
  • D

Q9:

In the given figure, the diameter of circle 𝑀 is 𝐴 𝐡 . If π‘š ∠ 𝐴 𝐡 𝐷 = 5 8 ∘ , what is π‘š ∠ 𝐷 𝐸 𝐡 ?

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

Q10:

Given that 𝐴 𝐡 is a diameter in the circle 𝑀 , and π‘š ∠ 𝐡 𝑀 𝐷 = 5 9 ∘ , find π‘š ∠ 𝐴 𝐢 𝐷 in degrees.

Q11:

Find .

  • A
  • B
  • C
  • D

Q12:

Given that and , find .

  • A
  • B
  • C
  • D

Q13:

Find π‘š ∠ 𝐡 𝐢 𝐷 and π‘š ∠ 𝐡 𝐴 𝐷 .

  • A π‘š ∠ 𝐡 𝐢 𝐷 = 1 2 3 ∘ , π‘š ∠ 𝐡 𝐴 𝐷 = 5 7 ∘
  • B π‘š ∠ 𝐡 𝐢 𝐷 = 1 1 4 ∘ , π‘š ∠ 𝐡 𝐴 𝐷 = 6 6 ∘
  • C π‘š ∠ 𝐡 𝐢 𝐷 = 6 6 ∘ , π‘š ∠ 𝐡 𝐴 𝐷 = 1 1 4 ∘
  • D π‘š ∠ 𝐡 𝐢 𝐷 = 5 7 ∘ , π‘š ∠ 𝐡 𝐴 𝐷 = 1 2 3 ∘

Q14:

Given that π‘š ∠ 𝐴 𝐡 𝐢 = 3 0 . 5 ∘ , find π‘š ∠ 𝐡 𝐷 𝐢 .

Q15:

Given that , find .

  • A
  • B
  • C
  • D

Q16:

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

  • A
  • B
  • C
  • D

Q17:

In the figure, 𝑀 is the center of the circle, and ∠ 𝑀 is the nonreflex angle at 𝑀 . Given that π‘š ∠ 𝑀 βˆ’ π‘š ∠ 𝐴 = 7 5 ∘ , find π‘š ∠ 𝐴 .

  • A 1 5 0 ∘
  • B 3 7 . 5 ∘
  • C 1 0 5 ∘
  • D 7 5 ∘

Q18:

Given that π‘š ∠ 𝐴 = 4 6 . 5 ∘ , find π‘₯ .

Q19:

Given that π‘š ∠ 𝐴 𝐡 𝐢 = 2 7 ∘ , and π‘š ∠ 𝐡 𝐷 𝐴 = 6 2 ∘ , find π‘š ∠ 𝐡 𝐷 𝐢 and π‘š ∠ 𝐡 𝐢 𝐷 .

  • A π‘š ∠ 𝐡 𝐷 𝐢 = 1 1 2 ∘ , π‘š ∠ 𝐡 𝐢 𝐷 = 1 7 8 ∘
  • B π‘š ∠ 𝐡 𝐷 𝐢 = 5 6 ∘ , π‘š ∠ 𝐡 𝐢 𝐷 = 8 9 ∘
  • C π‘š ∠ 𝐡 𝐷 𝐢 = 8 9 ∘ , π‘š ∠ 𝐡 𝐢 𝐷 = 2 7 ∘
  • D π‘š ∠ 𝐡 𝐷 𝐢 = 8 9 ∘ , π‘š ∠ 𝐡 𝐢 𝐷 = 5 6 ∘

Q20:

Find π‘₯ .

Q21:

Find π‘₯ + 𝑦 .

Q22:

In the figure, 𝐴 𝐸 intersects the circle at 𝐷 and 𝐸 , and 𝐴 𝐢 intersects the circle at 𝐡 and 𝐢 . Given that 𝐴 𝐡 = 𝐡 𝐸 , find π‘š ∠ 𝐢 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 π‘š ∠ 𝐴 𝐡 𝐢 .

Q25:

In the figure, 𝑂 is the center and π‘š ∠ 𝑂 𝐴 𝐡 = 5 9 . 5 ∘ .

What is the measure of angle 𝐴 𝑂 𝐡 ?

What is the measure of angle 𝐴 𝐢 𝐡 ?

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