Lesson Worksheet: Properties of Cyclic Quadrilaterals Mathematics

In this worksheet, we will practice using cyclic quadrilateral properties to find missing angles and identifying whether a quadrilateral is cyclic or not.

Q1:

Is 𝐴𝐵𝐶𝐷 a cyclic quadrilateral?

  • ANo
  • BYes

Q2:

Determine 𝑚∠𝐵𝐶𝐷.

Q3:

In cyclic quadrilateral 𝐴𝐵𝐶𝐷, if 𝑚∠𝐶=121∘, what is 𝑚∠𝐴?

Q4:

Is 𝐴𝐵𝐶𝐷 a cyclic quadrilateral?

  • ANo
  • BYes

Q5:

Given that 𝐴𝐵𝐶𝐷 is a cyclic quadrilateral, find 𝑚∠𝐵𝐴𝐶.

Q6:

Find 𝑚∠𝐵𝐶𝐷.

Q7:

Find 𝑚∠𝐵.

Q8:

Find 𝑚∠𝐸𝐶𝐹 and 𝑚∠𝐴𝐵𝐹.

  • A𝑚∠𝐸𝐶𝐹=104∘, 𝑚∠𝐴𝐵𝐹=80∘
  • B𝑚∠𝐸𝐶𝐹=80∘, 𝑚∠𝐴𝐵𝐹=76∘
  • C𝑚∠𝐸𝐶𝐹=76∘, 𝑚∠𝐴𝐵𝐹=80∘
  • D𝑚∠𝐸𝐶𝐹=100∘, 𝑚∠𝐴𝐵𝐹=104∘
  • E𝑚∠𝐸𝐶𝐹=76∘, 𝑚∠𝐴𝐵𝐹=100∘

Q9:

𝐴𝐵𝐶𝐷 is a cyclic quadrilateral with 𝑚∠𝐵𝐴𝐶=58∘ and 𝑚∠𝐴𝐷𝐸=87∘. What is 𝑚∠𝐵𝐶𝐴?

Q10:

Is the quadrilateral 𝐴𝐵𝐶𝐷 cyclic?

  • ANo
  • BYes

Q11:

Find the values of 𝑥 and 𝑦.

  • A𝑥=28, 𝑦=68
  • B𝑥=28, 𝑦=56
  • C𝑥=17, 𝑦=68
  • D𝑥=17, 𝑦=56

Q12:

Given that 𝑚∠𝐷𝐶𝐻=92∘, 𝑚∠𝐵𝐴𝐷=4𝑥∘, and 𝑚∠𝐶𝐷𝐴=2𝑦∘, find 𝑥+𝑦.

Q13:

In a cyclic quadrilateral 𝐴𝐵𝐶𝐷, if 𝑚∠𝐴=3𝑚∠𝐵=2𝑚∠𝐶, find 𝑚∠𝐷.

Q14:

Given that 𝑚∠𝐴=𝑦∘, 𝑚∠𝐵=(4𝑥−3)∘, and 𝑚∠𝐶=5𝑥∘, find the values of 𝑥 and 𝑦.

  • A𝑥=23, 𝑦=89
  • B𝑥=20, 𝑦=80
  • C𝑥=30, 𝑦=150
  • D𝑥=17, 𝑦=95
  • E𝑥=13, 𝑦=125

Q15:

Calculate the values of 𝑥 and 𝑦.

  • A𝑥=90, 𝑦=90
  • B𝑥=90, 𝑦=10
  • C𝑥=180, 𝑦=20
  • D𝑥=10, 𝑦=90

Q16:

Is 𝐴𝐵𝐶𝐷 a cyclic quadrilateral?

  • AYes
  • BNo

Q17:

In the figure, 𝐴𝐵𝐶𝐷 is a quadrilateral with 𝑚∠𝐴𝐵𝐶=117∘ and 𝑚∠𝐴𝐶𝐵=32.5∘. What is 𝑚∠𝐵𝐷𝐶?

Q18:

Given that 𝐴𝐵𝐶𝐷 is a cyclic quadrilateral, 𝑚∠𝐴𝐶𝐵=70∘, and 𝐴𝐵=𝐴𝐶, find 𝑚∠𝐵𝐷𝐶.

Q19:

Find the remaining internal angles of quadrilateral 𝐴𝐵𝐶𝐷.

  • A𝑚∠𝐴𝐵𝐶=77∘, 𝑚∠𝐶=150∘, 𝑚∠𝐶𝐷𝐴=47∘
  • B𝑚∠𝐴𝐵𝐶=150∘, 𝑚∠𝐶=103∘, 𝑚∠𝐶𝐷𝐴=77∘
  • C𝑚∠𝐴𝐵𝐶=103∘, 𝑚∠𝐶=77∘, 𝑚∠𝐶𝐷𝐴=73∘
  • D𝑚∠𝐴𝐵𝐶=133∘, 𝑚∠𝐶=77∘, 𝑚∠𝐶𝐷𝐴=47∘
  • E𝑚∠𝐴𝐵𝐶=107∘, 𝑚∠𝐶=77∘, 𝑚∠𝐶𝐷𝐴=73∘

Q20:

Find 𝑚∠𝐸𝑀𝑁, given that 𝐿𝑀𝑁𝐸 is a cyclic quadrilateral with 𝑚∠𝑀𝐿𝐸=64∘ and 𝑚∠𝑀𝐸𝑁=38∘.

Q21:

If 𝐴𝐵𝐶𝐷 is a cyclic quadrilateral, where 𝑚∠𝐵=54𝑚∠𝐷, find 𝑚∠𝐵.

Q22:

𝐴𝐵𝐶𝐷 is a cyclic quadrilateral.

Work out the measure of ∠𝐵𝐶𝐷.

Work out the measure of ∠𝐶𝐷𝐴.

Q23:

Find 𝑚∠𝐴 and 𝑚∠𝐷.

  • A𝑚∠𝐴=56∘, 𝑚∠𝐷=124∘
  • B𝑚∠𝐴=62∘, 𝑚∠𝐷=124∘
  • C𝑚∠𝐴=34∘, 𝑚∠𝐷=146∘
  • D𝑚∠𝐴=62∘, 𝑚∠𝐷=56∘
  • E𝑚∠𝐴=56∘, 𝑚∠𝐷=118∘

Q24:

Given that 𝐴𝐵𝐶𝐷 is a cyclic quadrilateral and 𝑚∠𝐵𝐷𝐴=46∘, find 𝑚∠𝐴𝐶𝐵.

Q25:

Find the measures of the interior angles of the quadrilateral 𝐴𝐵𝐶𝐷.

  • A𝑚∠𝐴=29∘, 𝑚∠𝐵=26.5∘, 𝑚∠𝐶=151∘, 𝑚∠𝐷=153.5∘
  • B𝑚∠𝐴=53∘, 𝑚∠𝐵=58∘, 𝑚∠𝐶=127∘, 𝑚∠𝐷=122∘
  • C𝑚∠𝐴=127∘, 𝑚∠𝐵=122∘, 𝑚∠𝐶=119∘, 𝑚∠𝐷=124.5∘
  • D𝑚∠𝐴=61∘, 𝑚∠𝐵=55.5∘, 𝑚∠𝐶=119∘, 𝑚∠𝐷=124.5∘

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