Lesson Worksheet: Inscribed Angles Subtended by the Same Arc Mathematics

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

Q1:

Given that 𝑚∠𝐵𝐴𝐷=36∘ and 𝑚∠𝐶𝐵𝐴=37∘, find 𝑚∠𝐵𝐶𝐷 and 𝑚∠𝐶𝐷𝐴.

  • A𝑚∠𝐵𝐶𝐷=74∘, 𝑚∠𝐶𝐷𝐴=72∘
  • B𝑚∠𝐵𝐶𝐷=37∘, 𝑚∠𝐶𝐷𝐴=36∘
  • C𝑚∠𝐵𝐶𝐷=36∘, 𝑚∠𝐶𝐷𝐴=37∘
  • D𝑚∠𝐵𝐶𝐷=72∘, 𝑚∠𝐶𝐷𝐴=74∘

Q2:

Given that 𝑚∠𝐴𝐵𝐷=44∘, and 𝑚∠𝐶𝐸𝐴=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 𝑚∠𝐵𝐴𝐷=(2𝑥+2)∘ and 𝑚∠𝐵𝐶𝐷=(𝑥+18)∘, determine the value of 𝑥.

Q4:

Given that 𝑚∠𝐴𝐸𝐶=36∘ and 𝑚∠𝐵𝐴𝐷=(4𝑥−8)∘, determine the value of 𝑥.

Q5:

Given that 𝑚∠𝐹𝐸𝐷=14∘ and 𝑚∠𝐶𝐵𝐴=(2𝑥−96)∘, calculate the value of 𝑥.

Q6:

In the figure, 𝐴𝐸 and 𝐵𝐶 pass through the center of the circles. Given that 𝑚∠𝐹𝐸𝐷=50∘ and 𝑚∠𝐶𝐵𝐴=(2𝑥−10)∘, find 𝑥.

Q7:

In the following figure, 𝐵𝐶 is a diameter of the circle, 𝑚∠𝐴𝐶𝐵=𝑚∠𝐶𝐷𝐸, 𝑚∠𝐵𝐷=42∘, and 𝐸 is the midpoint of 𝐶𝐷. Find 𝑚∠𝐴𝐶.

Q8:

Given that 𝑚∠𝐴𝐵𝐶=27∘, and 𝑚∠𝐵𝐷𝐴=62∘, find 𝑚∠𝐵𝐷𝐶 and 𝑚∠𝐵𝐶𝐷.

  • A𝑚∠𝐵𝐷𝐶=89∘, 𝑚∠𝐵𝐶𝐷=27∘
  • B𝑚∠𝐵𝐷𝐶=112∘, 𝑚∠𝐵𝐶𝐷=178∘
  • C𝑚∠𝐵𝐷𝐶=89∘, 𝑚∠𝐵𝐶𝐷=56∘
  • D𝑚∠𝐵𝐷𝐶=56∘, 𝑚∠𝐵𝐶𝐷=89∘

Q9:

Given that 𝐴𝐵 is a diameter of the circle and 𝐷𝐶∥𝐴𝐵, find 𝑚∠𝐴𝐸𝐷.

Q10:

Given that 𝑚∠𝐵𝐶𝐴=61∘ and 𝑚∠𝐷𝐴𝐵=98∘, can a circle pass through the points 𝐴, 𝐵, 𝐶, and 𝐷?

  • ANo
  • BYes

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