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 π‘šβˆ π΄π‘€π·=84∘ and π‘šβˆ π΅πΆπ΄=(𝑧+14)∘, determine the value of 𝑧.

Q2:

Given that π‘šβˆ π΄π΅π·=44∘, and π‘šβˆ πΆπΈπ΄=72∘, find π‘₯, 𝑦 and 𝑧.

  • Aπ‘₯=44∘, 𝑦=54∘, 𝑧=54∘
  • Bπ‘₯=44∘, 𝑦=64∘, 𝑧=64∘
  • Cπ‘₯=54∘, 𝑦=54∘, 𝑧=44∘
  • Dπ‘₯=64∘, 𝑦=44∘, 𝑧=44∘

Q3:

From the figure, what is π‘₯?

Q4:

Given that π‘šβˆ π‘€π΄πΆ=48∘, find 𝐿.

Q5:

Given that π‘šβˆ π΅π΄πΆ=89∘, find π‘šβˆ π‘₯.

Q6:

In the given figure, the diameter of circle 𝑀 is 𝐴𝐡. If π‘šβˆ π΄π΅π·=58∘, what is π‘šβˆ π·πΈπ΅?

  • A116∘
  • B64∘
  • C32∘
  • D58∘

Q7:

Given that 𝐴𝐡 is a diameter in the circle 𝑀, and π‘šβˆ π΅π‘€π·=59∘, find π‘šβˆ π΄πΆπ· in degrees.

Q8:

Given that 𝐡∈𝐷𝐢 and 𝐴𝐡=𝐷𝐡, find π‘šβˆ π·.

Q9:

Given that π‘šβˆ π΅π΄π·=105∘, find π‘šβˆ π‘€π΅πΆ.

Q10:

Given that 𝐴𝐡 is a diameter of the circle and 𝐷𝐢βˆ₯𝐴𝐡, find π‘šβˆ π΄πΈπ·.

Q11:

In the figure, 𝑀 is the center of the circle, and βˆ π‘€ is the nonreflex angle at 𝑀. Given that π‘šβˆ π‘€βˆ’π‘šβˆ π΄=75∘, find π‘šβˆ π΄.

Q12:

Given that π‘šβˆ π΄=46.5∘, find π‘₯.

Q13:

Given that π‘šβˆ π΄π΅πΆ=27∘, and π‘šβˆ π΅π·π΄=62∘, find π‘šβˆ π΅π·πΆ and π‘šβˆ π΅πΆπ·.

  • Aπ‘šβˆ π΅π·πΆ=89∘, π‘šβˆ π΅πΆπ·=27∘
  • Bπ‘šβˆ π΅π·πΆ=112∘, π‘šβˆ π΅πΆπ·=178∘
  • Cπ‘šβˆ π΅π·πΆ=89∘, π‘šβˆ π΅πΆπ·=56∘
  • Dπ‘šβˆ π΅π·πΆ=56∘, π‘šβˆ π΅πΆπ·=89∘

Q14:

Find π‘₯.

Q15:

Find π‘₯+𝑦.

Q16:

In the figure, 𝐴𝐸 intersects the circle at 𝐷 and 𝐸, and 𝐴𝐢 intersects the circle at 𝐡 and 𝐢. Given that 𝐴𝐡=𝐡𝐸, find π‘šβˆ πΆπ·πΈ.

Q17:

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

Q18:

Find π‘šβˆ π΄π΅πΆ.

Q19:

In the figure, 𝑂 is the center and π‘šβˆ π‘‚π΄π΅=59.5∘.

What is the measure of angle 𝐴𝑂𝐡?

What is the measure of angle 𝐴𝐢𝐡?

Q20:

Given that π‘šβˆ πΆπ΅π΄=68∘, find π‘šβˆ π‘₯.

Q21:

Find π‘šβˆ π΅πΈπ΄.

Q22:

Determine the type of an inscribed angle subtended by an arc that is 29 of the circle.

  • Aan acute angle
  • Ban obtuse angle
  • Ca right angle

Q23:

Given that π‘šβˆ π΄πΈπΆ=34∘ and 𝐡𝐸=𝐡𝐢, find π‘šβˆ π΅π΄π·.

Q24:

Find π‘šπ΄π·.

Q25:

Given that 𝐴𝐡=𝐴𝐷=𝐴𝐢, find π‘šβˆ π΅πΆπ·.

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