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.


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


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


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


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


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


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


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


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


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


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

  • ANo
  • BYes

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