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Worksheet: Properties of Cyclic Quadrilaterals

In this worksheet, we will practice identifying whether a quadrilateral is cyclic and using cyclic quadrilateral properties to find a missing angle.

Q1:

Find π‘š ∠ 𝐡 𝐢 𝐷 .

Q2:

Is a cyclic quadrilateral?

  • Ano
  • Byes

Q3:

Is a cyclic quadrilateral?

  • Ayes
  • Bno

Q4:

Is a cyclic quadrilateral?

  • Ayes
  • Bno

Q5:

Is a cyclic quadrilateral?

  • Ano
  • Byes

Q6:

𝐴 𝐡 𝐢 𝐷 is a cyclic quadrilateral with π‘š ∠ 𝐡 𝐴 𝐢 = 5 8 ∘ and π‘š ∠ 𝐴 𝐷 𝐸 = 8 7 ∘ . What is π‘š ∠ 𝐡 𝐢 𝐴 ?

Q7:

Is the quadrilateral 𝐴 𝐡 𝐢 𝐷 cyclic?

  • Ayes
  • Bno

Q8:

Find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 1 7 , 𝑦 = 6 8
  • B π‘₯ = 2 8 , 𝑦 = 6 8
  • C π‘₯ = 1 7 , 𝑦 = 5 6
  • D π‘₯ = 2 8 , 𝑦 = 5 6

Q9:

Given that π‘š ∠ 𝐷 𝐢 𝐻 = 9 2 ∘ , π‘š ∠ 𝐡 𝐴 𝐷 = 4 π‘₯ ∘ , and π‘š ∠ 𝐢 𝐷 𝐴 = 2 𝑦 ∘ , find π‘₯ + 𝑦 .

Q10:

In a cyclic quadrilateral 𝐴 𝐡 𝐢 𝐷 , if π‘š ∠ 𝐴 = 3 π‘š ∠ 𝐡 = 2 π‘š ∠ 𝐢 , find π‘š ∠ 𝐷 .

Q11:

Given that π‘š ∠ 𝐴 = 𝑦 ∘ , π‘š ∠ 𝐡 = ( 4 π‘₯ βˆ’ 3 ) ∘ , and π‘š ∠ 𝐢 = 5 π‘₯ ∘ , find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 3 0 , 𝑦 = 1 5 0
  • B π‘₯ = 2 0 , 𝑦 = 8 0
  • C π‘₯ = 2 3 , 𝑦 = 8 9
  • D π‘₯ = 1 7 , 𝑦 = 9 5
  • E π‘₯ = 1 3 , 𝑦 = 1 2 5

Q12:

Calculate the values of π‘₯ and 𝑦 .

  • A π‘₯ = 9 0 , 𝑦 = 9 0
  • B π‘₯ = 1 8 0 , 𝑦 = 2 0
  • C π‘₯ = 1 0 , 𝑦 = 9 0
  • D π‘₯ = 9 0 , 𝑦 = 1 0

Q13:

Is 𝐴 𝐡 𝐢 𝐷 a cyclic quadrilateral?

  • Ayes
  • Bno

Q14:

In the figure, 𝐴 𝐡 𝐢 𝐷 is a quadrilateral with π‘š ∠ 𝐴 𝐡 𝐢 = 1 1 7 ∘ and π‘š ∠ 𝐴 𝐢 𝐡 = 3 2 . 5 ∘ . What is π‘š ∠ 𝐡 𝐷 𝐢 ?

Q15:

Find π‘š ∠ 𝐸 𝐢 𝐹 and π‘š ∠ 𝐴 𝐡 𝐹 .

  • A π‘š ∠ 𝐸 𝐢 𝐹 = 7 6 ∘ , π‘š ∠ 𝐴 𝐡 𝐹 = 1 0 0 ∘
  • B π‘š ∠ 𝐸 𝐢 𝐹 = 1 0 0 ∘ , π‘š ∠ 𝐴 𝐡 𝐹 = 1 0 4 ∘
  • C π‘š ∠ 𝐸 𝐢 𝐹 = 1 0 4 ∘ , π‘š ∠ 𝐴 𝐡 𝐹 = 8 0 ∘
  • D π‘š ∠ 𝐸 𝐢 𝐹 = 8 0 ∘ , π‘š ∠ 𝐴 𝐡 𝐹 = 7 6 ∘
  • E π‘š ∠ 𝐸 𝐢 𝐹 = 7 6 ∘ , π‘š ∠ 𝐴 𝐡 𝐹 = 8 0 ∘

Q16:

Find π‘š ∠ 𝐸 𝐢 𝐹 and π‘š ∠ 𝐴 𝐡 𝐹 .

  • A π‘š ∠ 𝐸 𝐢 𝐹 = 9 2 ∘ , π‘š ∠ 𝐴 𝐡 𝐹 = 1 0 2 ∘
  • B π‘š ∠ 𝐸 𝐢 𝐹 = 1 0 2 ∘ , π‘š ∠ 𝐴 𝐡 𝐹 = 8 8 ∘
  • C π‘š ∠ 𝐸 𝐢 𝐹 = 8 8 ∘ , π‘š ∠ 𝐴 𝐡 𝐹 = 7 8 ∘
  • D π‘š ∠ 𝐸 𝐢 𝐹 = 7 8 ∘ , π‘š ∠ 𝐴 𝐡 𝐹 = 9 2 ∘
  • E π‘š ∠ 𝐸 𝐢 𝐹 = 9 2 ∘ , π‘š ∠ 𝐴 𝐡 𝐹 = 7 8 ∘

Q17:

Determine π‘š ∠ 𝐡 𝐢 𝐷 .

  • A 1 5 6 ∘
  • B 7 8 ∘
  • C 2 5 8 ∘
  • D 1 0 2 ∘
  • E 3 9 ∘

Q18:

Determine π‘š ∠ 𝐡 𝐢 𝐷 .

  • A 2 2 0 ∘
  • B 1 1 0 ∘
  • C 2 9 0 ∘
  • D 7 0 ∘
  • E 5 5 ∘

Q19:

Determine π‘š ∠ 𝐡 𝐢 𝐷 .

  • A 2 5 0 ∘
  • B 1 2 5 ∘
  • C 3 0 5 ∘
  • D 5 5 ∘
  • E 6 2 . 5 ∘

Q20:

In cyclic quadrilateral 𝐴 𝐡 𝐢 𝐷 , if π‘š ∠ 𝐢 = 1 2 1 ∘ , what is π‘š ∠ 𝐴 ?

Q21:

Given that is a cyclic quadrilateral, find .

  • A
  • B
  • C
  • D

Q22:

Is 𝐴 𝐡 𝐢 𝐷 a cyclic quadrilateral?

  • Ayes
  • Bno

Q23:

Is 𝐴 𝐡 𝐢 𝐷 a cyclic quadrilateral?

  • Ano
  • Byes

Q24:

Is 𝐴 𝐡 𝐢 𝐷 a cyclic quadrilateral?

  • Ayes
  • Bno

Q25:

Find .

  • A
  • B
  • C
  • D

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