Worksheet: Cyclic Quadrilaterals

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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.

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

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.

  • A 𝑚 ∠ 𝐸 𝐶 𝐹 = 1 0 4 ∘ , 𝑚 ∠ 𝐴 𝐵 𝐹 = 8 0 ∘
  • B 𝑚 ∠ 𝐸 𝐶 𝐹 = 8 0 ∘ , 𝑚 ∠ 𝐴 𝐵 𝐹 = 7 6 ∘
  • C 𝑚 ∠ 𝐸 𝐶 𝐹 = 7 6 ∘ , 𝑚 ∠ 𝐴 𝐵 𝐹 = 8 0 ∘
  • D 𝑚 ∠ 𝐸 𝐶 𝐹 = 1 0 0 ∘ , 𝑚 ∠ 𝐴 𝐵 𝐹 = 1 0 4 ∘
  • E 𝑚 ∠ 𝐸 𝐶 𝐹 = 7 6 ∘ , 𝑚 ∠ 𝐴 𝐵 𝐹 = 1 0 0 ∘

Q9:

𝐴 𝐵 𝐶 𝐷 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.

  • A 𝑥 = 2 8 , 𝑦 = 6 8
  • B 𝑥 = 2 8 , 𝑦 = 5 6
  • C 𝑥 = 1 7 , 𝑦 = 6 8
  • D 𝑥 = 1 7 , 𝑦 = 5 6

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.

  • A 𝑥 = 2 3 , 𝑦 = 8 9
  • B 𝑥 = 2 0 , 𝑦 = 8 0
  • C 𝑥 = 3 0 , 𝑦 = 1 5 0
  • D 𝑥 = 1 7 , 𝑦 = 9 5
  • E 𝑥 = 1 3 , 𝑦 = 1 2 5

Q15:

Calculate the values of 𝑥 and 𝑦.

  • A 𝑥 = 9 0 , 𝑦 = 9 0
  • B 𝑥 = 9 0 , 𝑦 = 1 0
  • C 𝑥 = 1 8 0 , 𝑦 = 2 0
  • D 𝑥 = 1 0 , 𝑦 = 9 0

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.

  • A 𝑚 ∠ 𝐴 𝐵 𝐶 = 7 7 ∘ , 𝑚 ∠ 𝐶 = 1 5 0 ∘ , 𝑚 ∠ 𝐶 𝐷 𝐴 = 4 7 ∘
  • B 𝑚 ∠ 𝐴 𝐵 𝐶 = 1 5 0 ∘ , 𝑚 ∠ 𝐶 = 1 0 3 ∘ , 𝑚 ∠ 𝐶 𝐷 𝐴 = 7 7 ∘
  • C 𝑚 ∠ 𝐴 𝐵 𝐶 = 1 0 3 ∘ , 𝑚 ∠ 𝐶 = 7 7 ∘ , 𝑚 ∠ 𝐶 𝐷 𝐴 = 7 3 ∘
  • D 𝑚 ∠ 𝐴 𝐵 𝐶 = 1 3 3 ∘ , 𝑚 ∠ 𝐶 = 7 7 ∘ , 𝑚 ∠ 𝐶 𝐷 𝐴 = 4 7 ∘
  • E 𝑚 ∠ 𝐴 𝐵 𝐶 = 1 0 7 ∘ , 𝑚 ∠ 𝐶 = 7 7 ∘ , 𝑚 ∠ 𝐶 𝐷 𝐴 = 7 3 ∘

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:

Is 𝐴𝐵𝐶𝐷 a cyclic quadrilateral?

  • Ano
  • Byes

Q23:

𝐴 𝐵 𝐶 𝐷 is a cyclic quadrilateral.

Work out the measure of ∠𝐵𝐶𝐷.

Work out the measure of ∠𝐶𝐷𝐴.

Q24:

Is there a circle passing through the vertices of the quadrilateral 𝐴𝐵𝐶𝐷?

  • Ano
  • Byes

Q25:

In the figure below, 𝑚∠𝐴𝐷𝐸=26.9∘, 𝑚∠𝐴𝐸𝐵=82.9∘, and 𝑚∠𝐴𝐵𝐸=59.1∘. Is 𝐴𝐵𝐶𝐷 a cyclic quadrilateral?

  • Ano
  • Byes

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