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Lesson: Properties of Cyclic Quadrilaterals

In this lesson, we will learn how to identify whether a quadrilateral is cyclic and use cyclic quadrilateral properties to find a missing angle.

Sample Question Videos

03:44
04:14

Worksheet • 25 Questions • 2 Videos

Q1:

Is a cyclic quadrilateral?

  • Ayes
  • Bno

Q2:

Determine .

  • A
  • B
  • C
  • D
  • E

Q3:

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

Q4:

Is 𝐴 𝐡 𝐢 𝐷 a cyclic quadrilateral?

  • Ano
  • Byes

Q5:

Given that 𝐴 𝐡 𝐢 𝐷 is a cyclic quadrilateral, find π‘š ∠ 𝐡 𝐴 𝐢 .

Q6:

Find π‘š ∠ 𝐡 𝐢 𝐷 .

Q7:

Find π‘š ∠ 𝐡 .

Q8:

Find π‘š ∠ 𝐸 𝐢 𝐹 and π‘š ∠ 𝐴 𝐡 𝐹 .

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

Q9:

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 ?

Q10:

Is the quadrilateral 𝐴 𝐡 𝐢 𝐷 cyclic?

  • Ano
  • Byes

Q11:

Find the values of π‘₯ and 𝑦 .

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

Q12:

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 .

Q13:

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

Q14:

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

Q15:

Calculate the values of π‘₯ and 𝑦 .

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

Q16:

Is 𝐴 𝐡 𝐢 𝐷 a cyclic quadrilateral?

  • Ano
  • Byes

Q17:

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 ?

Q18:

Given that 𝐴 𝐡 𝐢 𝐷 is a cyclic quadrilateral, π‘š ∠ 𝐴 𝐢 𝐡 = 7 0 ∘ , and 𝐴 𝐡 = 𝐴 𝐢 , find π‘š ∠ 𝐡 𝐷 𝐢 .

Q19:

Find the remaining internal angles of quadrilateral 𝐴 𝐡 𝐢 𝐷 .

  • A π‘š ∠ 𝐴 𝐡 𝐢 = 1 0 7 ∘ , π‘š ∠ 𝐢 = 7 7 ∘ , π‘š ∠ 𝐢 𝐷 𝐴 = 7 3 ∘
  • B π‘š ∠ 𝐴 𝐡 𝐢 = 1 3 3 ∘ , π‘š ∠ 𝐢 = 7 7 ∘ , π‘š ∠ 𝐢 𝐷 𝐴 = 4 7 ∘
  • C π‘š ∠ 𝐴 𝐡 𝐢 = 1 0 3 ∘ , π‘š ∠ 𝐢 = 7 7 ∘ , π‘š ∠ 𝐢 𝐷 𝐴 = 7 3 ∘
  • D π‘š ∠ 𝐴 𝐡 𝐢 = 1 5 0 ∘ , π‘š ∠ 𝐢 = 1 0 3 ∘ , π‘š ∠ 𝐢 𝐷 𝐴 = 7 7 ∘
  • E π‘š ∠ 𝐴 𝐡 𝐢 = 7 7 ∘ , π‘š ∠ 𝐢 = 1 5 0 ∘ , π‘š ∠ 𝐢 𝐷 𝐴 = 4 7 ∘

Q20:

Find π‘š ∠ 𝐸 𝑀 𝑁 , given that 𝐿 𝑀 𝑁 𝐸 is a cyclic quadrilateral with π‘š ∠ 𝑀 𝐿 𝐸 = 6 4 ∘ and π‘š ∠ 𝑀 𝐸 𝑁 = 3 8 ∘ .

Q21:

If 𝐴 𝐡 𝐢 𝐷 is a cyclic quadrilateral, where π‘š ∠ 𝐡 = 5 4 π‘š ∠ 𝐷 , find π‘š ∠ 𝐡 .

Q22:

Is 𝐴 𝐡 𝐢 𝐷 a cyclic quadrilateral?

  • Ano
  • Byes

Q23:

is a cyclic quadrilateral.

Work out the size of .

  • A
  • B
  • C
  • D
  • E

Work out the size of .

  • A
  • B
  • C
  • D
  • E

Q24:

Is there a circle passing through the vertices of the quadrilateral 𝐴 𝐡 𝐢 𝐷 ?

  • Ano
  • Byes

Q25:

In the figure below, π‘š ∠ 𝐴 𝐷 𝐸 = 2 6 . 9 ∘ , π‘š ∠ 𝐴 𝐸 𝐡 = 8 2 . 9 ∘ , and π‘š ∠ 𝐴 𝐡 𝐸 = 5 9 . 1 ∘ . Is 𝐴 𝐡 𝐢 𝐷 a cyclic quadrilateral?

  • Ayes
  • Bno
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