Worksheet: Cyclic Quadrilaterals

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 𝑚𝐵𝐶𝐷.

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

Q3:

In cyclic quadrilateral 𝐴𝐵𝐶𝐷, if 𝑚𝐶=121, what is 𝑚𝐴?

Q4:

Is 𝐴𝐵𝐶𝐷 a cyclic quadrilateral?

  • Ano
  • Byes

Q5:

Given that 𝐴𝐵𝐶𝐷 is a cyclic quadrilateral, find 𝑚𝐵𝐴𝐶.

Q6:

Find 𝑚𝐵𝐶𝐷.

Q7:

Find 𝑚𝐵.

Q8:

Find 𝑚𝐸𝐶𝐹 and 𝑚𝐴𝐵𝐹.

  • 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 𝑚𝐵𝐴𝐶=58 and 𝑚𝐴𝐷𝐸=87. What is 𝑚𝐵𝐶𝐴?

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 𝑚𝐷𝐶𝐻=92, 𝑚𝐵𝐴𝐷=4𝑥, and 𝑚𝐶𝐷𝐴=2𝑦, find 𝑥+𝑦.

Q13:

In a cyclic quadrilateral 𝐴𝐵𝐶𝐷, if 𝑚𝐴=3𝑚𝐵=2𝑚𝐶, find 𝑚𝐷.

Q14:

Given that 𝑚𝐴=𝑦, 𝑚𝐵=(4𝑥3), and 𝑚𝐶=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 𝑚𝐴𝐵𝐶=117 and 𝑚𝐴𝐶𝐵=32.5. What is 𝑚𝐵𝐷𝐶?

Q18:

Given that 𝐴𝐵𝐶𝐷 is a cyclic quadrilateral, 𝑚𝐴𝐶𝐵=70, and 𝐴𝐵=𝐴𝐶, find 𝑚𝐵𝐷𝐶.

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 𝑚𝐸𝑀𝑁, given that 𝐿𝑀𝑁𝐸 is a cyclic quadrilateral with 𝑚𝑀𝐿𝐸=64 and 𝑚𝑀𝐸𝑁=38.

Q21:

If 𝐴𝐵𝐶𝐷 is a cyclic quadrilateral, where 𝑚𝐵=54𝑚𝐷, find 𝑚𝐵.

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, 𝑚𝐴𝐷𝐸=26.9, 𝑚𝐴𝐸𝐵=82.9, and 𝑚𝐴𝐵𝐸=59.1. Is 𝐴𝐵𝐶𝐷 a cyclic quadrilateral?

  • Ano
  • Byes

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