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Lesson Worksheet: Inscribed Angles Subtended by the Same Arc Mathematics

In this worksheet, we will practice finding the measures of inscribed angles subtended by the same arc or by congruent arcs.

Q1:

Given that 𝑚𝐵𝐴𝐷=36 and 𝑚𝐶𝐵𝐴=37, find 𝑚𝐵𝐶𝐷 and 𝑚𝐶𝐷𝐴.

  • A𝑚𝐵𝐶𝐷=74, 𝑚𝐶𝐷𝐴=72
  • B𝑚𝐵𝐶𝐷=37, 𝑚𝐶𝐷𝐴=36
  • C𝑚𝐵𝐶𝐷=36, 𝑚𝐶𝐷𝐴=37
  • D𝑚𝐵𝐶𝐷=72, 𝑚𝐶𝐷𝐴=74

Q2:

Given that 𝑚𝐴𝐵𝐷=44, and 𝑚𝐶𝐸𝐴=72, find 𝑥, 𝑦 and 𝑧.

  • A𝑥=44, 𝑦=54, 𝑧=54
  • B𝑥=44, 𝑦=64, 𝑧=64
  • C𝑥=54, 𝑦=54, 𝑧=44
  • D𝑥=64, 𝑦=44, 𝑧=44

Q3:

If 𝑚𝐵𝐴𝐷=(2𝑥+2) and 𝑚𝐵𝐶𝐷=(𝑥+18), determine the value of 𝑥.

Q4:

Given that 𝑚𝐴𝐸𝐶=36 and 𝑚𝐵𝐴𝐷=(4𝑥8), determine the value of 𝑥.

Q5:

Given that 𝑚𝐹𝐸𝐷=14 and 𝑚𝐶𝐵𝐴=(2𝑥96), calculate the value of 𝑥.

Q6:

In the figure, 𝐴𝐸 and 𝐵𝐶 pass through the center of the circles. Given that 𝑚𝐹𝐸𝐷=50 and 𝑚𝐶𝐵𝐴=(2𝑥10), find 𝑥.

Q7:

In the following figure, 𝐵𝐶 is a diameter of the circle, 𝑚𝐴𝐶𝐵=𝑚𝐶𝐷𝐸, 𝑚𝐵𝐷=42, and 𝐸 is the midpoint of 𝐶𝐷. Find 𝑚𝐴𝐶.

Q8:

Given that 𝑚𝐴𝐵𝐶=27, and 𝑚𝐵𝐷𝐴=62, find 𝑚𝐵𝐷𝐶 and 𝑚𝐵𝐶𝐷.

  • A𝑚𝐵𝐷𝐶=89, 𝑚𝐵𝐶𝐷=27
  • B𝑚𝐵𝐷𝐶=112, 𝑚𝐵𝐶𝐷=178
  • C𝑚𝐵𝐷𝐶=89, 𝑚𝐵𝐶𝐷=56
  • D𝑚𝐵𝐷𝐶=56, 𝑚𝐵𝐶𝐷=89

Q9:

Given that 𝐴𝐵 is a diameter of the circle and 𝐷𝐶𝐴𝐵, find 𝑚𝐴𝐸𝐷.

Q10:

Given that 𝑚𝐵𝐶𝐴=61 and 𝑚𝐷𝐴𝐵=98, can a circle pass through the points 𝐴, 𝐵, 𝐶, and 𝐷?

  • ANo
  • BYes

This lesson includes 29 additional questions and 338 additional question variations for subscribers.

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