Lesson Worksheet: Inscribed Angles in a Circle Mathematics • 11th Grade

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In this worksheet, we will practice identifying theorems of finding the measure of an inscribed angle with respect to its subtended arc or central angle subtended by the same arc and the measures of inscribed angles in a semicircle.

Q1:

Find 𝑚∠𝐴𝐶𝐷.

Q2:

From the figure, what is 𝑥?

Q3:

Given that 𝑚∠𝐴𝑀𝐷=41.5∘, find 𝑚∠𝐵 in degrees.

Q4:

Find 𝑚∠𝐷𝐶𝐵.

Q5:

Given that 𝑚∠𝐵𝐴𝐶=(𝑥+15)∘, find 𝑥.

Q6:

Given that 𝐴𝐶=8cm and the radius =8cm, find the area of △𝐴𝐵𝐶 rounded to the nearest integer.

Q7:

In the figure, 𝐵𝐷 is a diameter. What is 𝑚∠𝐴𝐶𝐷?

Q8:

Given that 𝑚∠𝐶𝐴𝐵=64∘, find 𝑚∠𝐶𝐵𝐷.

Q9:

Given that 𝑚∠𝐶𝐴𝐵=31∘, find 𝑦 and 𝑥.

  • A𝑦=59, 𝑥=90
  • B𝑦=31, 𝑥=90
  • C𝑦=31, 𝑥=59
  • D𝑦=90, 𝑥=59

Q10:

Given that 𝑚∠𝐴𝐵𝐶=(6𝑥+15)∘ and 𝑚∠𝐶𝐴𝐵=(11𝑥−10)∘, find the value of 𝑥.

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