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Worksheet: Angles Formed by Lines Intersecting inside a Circle

Q1:

Given that π‘š ∠ 𝐡 𝐴 𝐢 = ( π‘₯ + 1 5 ) ∘ , find π‘₯ .

Q2:

Find π‘š ∠ 𝑦 .

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

Q3:

Find π‘š ∠ 𝐴 𝐡 𝐢 .

Q4:

Given that , and is the midpoint of , find .

  • A
  • B
  • C
  • D

Q5:

Find .

  • A
  • B
  • C
  • D

Q6:

Find the value of 𝑧 .

Q7:

Find .

  • A
  • B
  • C
  • D

Q8:

Find .

  • A
  • B
  • C

Q9:

If , find .

  • A
  • B
  • C
  • D

Q10:

Given that π‘š ∠ 𝐸 𝐴 𝐷 = 5 4 ∘ , find π‘š ∠ π‘₯ .

Q11:

In the figure, and are equal chords and and are their midpoints. Determine .

  • A
  • B
  • C
  • D

Q12:

Find π‘š ∠ π‘₯ .

Q13:

Find π‘š ∠ π‘₯ .

Q14:

Given that , find .

  • A
  • B
  • C
  • D

Q15:

Find the value of π‘₯ .

Q16:

Find the value of π‘₯ .

Q17:

Given that and are two equal chords in the circle , where and , find and the length of .

  • A , 86 cm
  • B , 43 cm
  • C , 86 cm
  • D , 43 cm

Q18:

Given that π‘š ∠ 𝐡 𝐢 𝐴 = 4 6 ∘ and π‘š ∠ 𝐡 𝑀 𝐴 = ( 𝑦 + 1 0 ) ∘ , find 𝑦 .

Q19:

Given that π‘Œ 𝑋 = 𝑀 𝐷 and π‘š ∠ 𝐡 𝐴 𝐢 = 5 2 ∘ , find π‘š ∠ 𝐴 𝐡 𝐢 .

Q20:

Find .

  • A
  • B
  • C
  • D

Q21:

Find the value of π‘₯ .

Q22:

Find π‘š ∠ 𝐷 𝑀 𝐸 .

Q23:

Find π‘š ∠ π‘₯ in the given figure.

Q24:

In the figure, determine .

  • A
  • B
  • C
  • D

Q25:

Given that 𝐴 𝐡 is a diameter in the circle 𝑀 , determine π‘š 𝐴 𝐢 and π‘š 𝐴 𝐷 .

  • A π‘š 𝐴 𝐢 = 4 8 ∘ , π‘š 𝐴 𝐷 = 1 6 9 ∘
  • B π‘š 𝐴 𝐢 = 1 2 1 ∘ , π‘š 𝐴 𝐷 = 4 8 ∘
  • C π‘š 𝐴 𝐢 = 1 6 9 ∘ , π‘š 𝐴 𝐷 = 4 8 ∘
  • D π‘š 𝐴 𝐢 = 4 8 ∘ , π‘š 𝐴 𝐷 = 1 2 1 ∘