Worksheet: Angles Formed by Lines Intersecting inside a Circle

In this worksheet, we will practice finding the measure of an angle that is formed by lines intersecting inside a circle.

Q1:

Given that 𝑚 𝐵 𝐴 𝐶 = ( 𝑥 + 1 5 ) , find 𝑥 .

Q2:

Find 𝑚 𝐴 𝐶 𝐷 .

Q3:

Find 𝑚 𝑦 .

  • A 1 0 3
  • B 5 0
  • C 9 7
  • D 1 0 0

Q4:

Find 𝑥 .

Q5:

Find the value of 𝑥 .

Q6:

Find 𝑚 𝑥 in the given figure.

Q7:

Find the value of 𝑧 .

Q8:

Find the value of 𝑥 .

Q9:

Find 𝑚 𝐴 𝐵 𝐶 .

Q10:

Given that 𝑚 𝐵 𝐶 𝐴 = 4 6 and 𝑚 𝐵 𝑀 𝐴 = ( 𝑦 + 1 0 ) , find 𝑦 .

Q11:

Given that 𝐴 𝐵 is a diameter in the circle 𝑀 , determine 𝑚 𝐴 𝐶 and 𝑚 𝐴 𝐷 .

  • A 𝑚 𝐴 𝐶 = 4 8 , 𝑚 𝐴 𝐷 = 1 6 9
  • B 𝑚 𝐴 𝐶 = 1 2 1 , 𝑚 𝐴 𝐷 = 4 8
  • C 𝑚 𝐴 𝐶 = 1 6 9 , 𝑚 𝐴 𝐷 = 4 8
  • D 𝑚 𝐴 𝐶 = 4 8 , 𝑚 𝐴 𝐷 = 1 2 1

Q12:

Given that 𝑌 𝑋 = 𝑀 𝐷 and 𝐵 𝐴 𝐶 = 5 2 , find 𝐴 𝐵 𝐶 .

Q13:

Find 𝑚 𝐷 𝑀 𝐸 .

Q14:

In the figure, determine 𝑚 𝐴 𝑂 𝐵 .

Q15:

Given that 𝑚 𝐶 𝐴 𝐵 = 3 9 , and 𝐸 is the midpoint of 𝐴 𝐶 , find 𝑚 𝐵 𝐹 𝐸 .

Q16:

Find 𝑚 𝐵 .

Q17:

Find 𝑚 𝐵 .

Q18:

Find 𝑚 𝐶 .

Q19:

If 𝑚 𝑌 𝑋 𝑀 = 2 8 . 5 , find 𝑚 𝐶 𝑌 𝑋 .

Q20:

Given that 𝑚 𝐸 𝐴 𝐷 = 5 4 , find 𝑚 𝑥 .

Q21:

In the figure, 𝐴 𝐵 and 𝐶 𝐷 are equal chords and 𝑋 and 𝑌 are their midpoints. Determine 𝑋 𝑀 𝑌 .

Q22:

Given that 𝑚 𝐵 = 6 9 , find 𝑚 𝐴 .

  • A 1 1 1
  • B 6 9
  • C 1 3 8
  • D 4 2

Q23:

Given that 𝐴 𝐵 and 𝐴 𝐶 are two equal chords in the circle 𝑀 , where 𝑚 𝐶 𝐴 𝐵 = 3 6 and 𝐷 𝐵 = 4 3 c m , find 𝑚 𝐷 𝑀 𝐸 and the length of 𝐸 𝐶 .

  • A 1 4 4 , 86 cm
  • B 1 0 8 , 43 cm
  • C 3 6 , 86 cm
  • D 1 4 4 , 43 cm

Q24:

Find 𝑚 𝑀 𝑋 𝑌 .

Q25:

What is 𝑚 𝑀 𝐴 𝐵 ?

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