Worksheet: Angles of Intersecting Lines in a Circle

In this worksheet, we will practice finding the measures of angles resulting from the intersection of two chords, two secants, or tangents and secants in a circle.

Q1:

Find the value of 𝑧.

Q2:

In the given figure, 𝑚𝐶𝐸𝑚𝐵𝐷=104. Determine 𝑚𝐴.

Q3:

Determine 𝑚𝐶𝐵.

Q4:

In the given figure, find 𝑚𝐴𝐶+𝑚𝐵𝐷.

Q5:

Find the value of 𝑥.

Q6:

Given that 𝑚𝐴=31, find 𝑥.

Q7:

Find 𝑥.

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

Q8:

Find 𝑥.

Q9:

Find 𝑚𝐵𝐴𝐶.

  • A 6 2
  • B 1 2 1
  • C 2 3 9
  • D 5 9
  • E 2 4 2

Q10:

Given that, in the shown figure, 𝑦=(𝑥2) and 𝑧=(2𝑥+2), determine the value of 𝑥.

Q11:

Given that 𝑚𝐶𝐴𝐵=76, find the value of 𝑥.

Q12:

Given that 𝐵𝐶 is a tangent to the circle, find 𝑚𝐴𝐵𝐶.

Q13:

Find 𝑥.

Q14:

The circle in the given figure has an arc with a measure of 88.

What is the measure of the central angle?

What is the measure of the inscribed angle?

What is the measure of the circumscribed angle?

Q15:

Find 𝑥.

Q16:

Find the value of 𝑥.

Q17:

Given that, in the shown figure, 𝑦=(𝑥4) and 𝑧=(2𝑥+2), determine the value of 𝑥.

Q18:

In the given figure, find 𝑚𝐴𝐶+𝑚𝐵𝐷.

Q19:

Find 𝑥.

  • A 1 8
  • B 3 6
  • C 1 5 2
  • D 1 0 4
  • E 7 6

Q20:

In the shown figure, 𝐸𝑇 is tangent to the circle, 𝐸𝐴=20, 𝐸𝐶=23, and 𝐶𝐷=13. Determine the lengths of 𝐸𝑇 and 𝐴𝐵.

  • A 𝐸 𝑇 = 6 2 3 , 𝐴 𝐵 = 1 3
  • B 𝐸 𝑇 = 4 3 , 𝐴 𝐵 = 1 3
  • C 𝐸 𝑇 = 2 3 , 𝐴 𝐵 = 2 0
  • D 𝐸 𝑇 = 6 2 3 , 𝐴 𝐵 = 1 0 7 5

Q21:

𝐴 𝐵 𝐶 𝐷 𝐸 is the regular pentagon drawn inside the circle 𝑀, 𝐴𝑋 is a tangent to the circle at 𝐴, and 𝐸𝑋 is a tangent to the circle at 𝐸. Find 𝑚𝐴𝑋𝐸.

Q22:

The point 𝐴 is outside a circle with centre 𝑀. The line between 𝐴 and 𝐶 intersects the circle at 𝐵 and 𝐶, and the line between 𝐴 and 𝐸 meets the circle at points 𝐷 and 𝐸. Given that 𝐶𝑀𝐸=130 and 𝐵𝑀𝐷=56, find 𝐴.

Q23:

Given that 𝐴𝐵 and 𝐴𝐶 are two tangents to the circle 𝑀, and 𝑚𝑀𝐴𝐶=21, determine 𝑚𝐶𝐴𝐵.

Q24:

Find 𝑥.

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

Q25:

Find 𝑥.

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