Lesson Worksheet: Inscribed Angles in a Circle Mathematics

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:

Given that 𝑚𝐴𝑀𝐷=84 and 𝑚𝐵𝐶𝐴=(𝑧+14), determine the value of 𝑧.

Q2:

From the figure, what is 𝑥?

Q3:

Given that 𝑚𝑀𝐴𝐶=48, find 𝐿.

Q4:

Given that 𝑚𝐵𝐴𝐶=89, find 𝑚𝑥.

Q5:

In the given figure, the diameter of circle 𝑀 is 𝐴𝐵. If 𝑚𝐴𝐵𝐷=58, what is 𝑚𝐷𝐸𝐵?

  • A116
  • B64
  • C32
  • D58

Q6:

Given that 𝐴𝐵 is a diameter in the circle 𝑀, and 𝑚𝐵𝑀𝐷=59, find 𝑚𝐴𝐶𝐷 in degrees.

Q7:

Given that 𝐵𝐷𝐶 and 𝐴𝐵=𝐷𝐵, find 𝑚𝐷.

Q8:

Given that 𝑚𝐵𝐴𝐷=105, find 𝑚𝑀𝐵𝐶.

Q9:

In the figure, 𝑀 is the center of the circle, and 𝑀 is the nonreflex angle at 𝑀. Given that 𝑚𝑀𝑚𝐴=75, find 𝑚𝐴.

Q10:

Given that 𝑚𝐴=46.5, find 𝑥.

Q11:

Find 𝑥.

Q12:

Find 𝑥+𝑦.

Q13:

In the figure, 𝐴𝐸 intersects the circle at 𝐷 and 𝐸, and 𝐴𝐶 intersects the circle at 𝐵 and 𝐶. Given that 𝐴𝐵=𝐵𝐸, find 𝑚𝐶𝐷𝐸.

Q14:

If the measure of an arc of a circle is 171, what is the measure of the inscribed angle subtended by that arc?

Q15:

Find 𝑚𝐴𝐵𝐶.

Q16:

In the figure, 𝑂 is the center and 𝑚𝑂𝐴𝐵=59.5.

What is the measure of angle 𝐴𝑂𝐵?

What is the measure of angle 𝐴𝐶𝐵?

Q17:

Given that 𝑚𝐶𝐵𝐴=68, find 𝑚𝑥.

Q18:

Find 𝑚𝐵𝐸𝐴.

Q19:

Determine the type of an inscribed angle subtended by an arc that is 29 of the circle.

  • Aan acute angle
  • Ban obtuse angle
  • Ca right angle

Q20:

Given that 𝑚𝐴𝐸𝐶=34 and 𝐵𝐸=𝐵𝐶, find 𝑚𝐵𝐴𝐷.

Q21:

Given that 𝐴𝐵=𝐴𝐷=𝐴𝐶, find 𝑚𝐵𝐶𝐷.

Q22:

Find 𝑥.

Q23:

Given that 𝑚𝐴𝑁𝐵=156, find 𝑚𝐶.

Q24:

Find 𝑚𝐷𝐶𝐵.

Q25:

Given that 𝐴𝐷 is a diameter in a circle with center 𝑀, find 𝑚𝐵𝑀𝐷 and 𝑚𝐷𝑀𝐶.

  • A𝑚𝐵𝑀𝐷=39, 𝑚𝐷𝑀𝐶=100
  • B𝑚𝐵𝑀𝐷=78, 𝑚𝐷𝑀𝐶=100
  • C𝑚𝐵𝑀𝐷=78, 𝑚𝐷𝑀𝐶=50
  • D𝑚𝐵𝑀𝐷=39, 𝑚𝐷𝑀𝐶=50

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