Worksheet: Applications of Angles in Semicircles

In this worksheet, we will practice applying the fact that the angle inscribed in a semicircle is a right angle, in a variety of questions.

Q1:

Find 𝑚 𝐴 .

Q2:

Given that 𝑚 𝐶 𝐴 𝐵 = 3 1 , find 𝑦 and 𝑥 .

  • A 𝑦 = 3 1 , 𝑥 = 9 0
  • B 𝑦 = 5 9 , 𝑥 = 9 0
  • C 𝑦 = 3 1 , 𝑥 = 5 9
  • D 𝑦 = 9 0 , 𝑥 = 5 9

Q3:

Find 𝑥 and 𝑦 .

  • A 𝑥 = 6 6 , 𝑦 = 1 1 4
  • B 𝑥 = 5 7 , 𝑦 = 3 3
  • C 𝑥 = 1 1 4 , 𝑦 = 6 6
  • D 𝑥 = 3 3 , 𝑦 = 5 7

Q4:

Given that 𝑚 𝐷 𝐴 𝐵 = 5 8 , find 𝑚 𝐶 𝐴 𝐵 .

  • A 7
  • B 2 9
  • C 6 5
  • D 3 3

Q5:

Given that 𝐴 𝑀 = 5 0 c m , find the length of 𝐵 𝐶 .

Q6:

Given that 𝐴 𝐵 𝐷 = 3 3 and 𝐶 𝐸 𝐵 = 6 7 , find 𝐶 𝐴 𝐵 and 𝐷 𝐴 𝐶 .

  • A 2 3 , 2 3
  • B 3 3 , 6 7
  • C 6 7 , 2 3
  • D 3 4 , 2 3

Q7:

Find 𝑚 𝐶 𝑀 𝐷 .

Q8:

Given that 𝐴 𝐵 𝐶 𝐷 is a rectangle, in which 𝐴 𝐷 = 1 0 c m , 𝐷 𝐶 = 7 c m , and 𝐶 𝐸 = 𝐶 𝐷 , find the length of 𝐴 𝐸 .

Q9:

Given that 𝑚 𝐵 𝐸 𝐷 = ( 3 𝑥 1 8 ) , find 𝑥 .

Q10:

Point 𝐴 is outside a circle centre 𝑀 , and 𝐴 𝑀 meets the circle in 𝐶 and 𝐷 . Suppose that 𝐴 𝐵 is tangent to the circle at 𝐵 and 𝐴 = 9 . What is 𝐵 𝐷 𝐶 ?

Q11:

In the given figure, is a diameter.

What is the size of angle ?

  • A
  • B
  • C
  • D
  • E

Given that the size of angle , find the size of angle .

  • A
  • B
  • C
  • D
  • E

Calculate the size of angle .

  • A
  • B
  • C
  • D
  • E

Q12:

Find 𝑚 𝐶 𝑀 𝐷 .

Q13:

Given that 𝑚 𝐷 𝐴 𝐵 = 8 4 , find 𝑚 𝐶 𝐴 𝐵 .

  • A 3 4
  • B 4 2
  • C 5 0
  • D 4 4

Q14:

Given that 𝑚 𝐷 𝐴 𝐵 = 7 6 , find 𝑚 𝐶 𝐴 𝐵 .

  • A 2 7
  • B 3 8
  • C 4 9
  • D 3 5

Q15:

Given that 𝐴 𝐵 𝐷 = 3 2 and 𝐶 𝐸 𝐵 = 6 3 , find 𝐶 𝐴 𝐵 and 𝐷 𝐴 𝐶 .

  • A 2 7 , 2 7
  • B 3 2 , 6 3
  • C 6 3 , 2 7
  • D 3 1 , 2 7

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