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Lesson: Applications of Angles in Semicircles

Sample Question Videos

Worksheet • 15 Questions • 1 Video

Q1:

Find π‘š ∠ 𝐴 .

Q2:

Given that π‘š ∠ 𝐢 𝐴 𝐡 = 3 1 ∘ , find 𝑦 and π‘₯ .

  • A 𝑦 = 9 0 , π‘₯ = 5 9
  • B 𝑦 = 5 9 , π‘₯ = 9 0
  • C 𝑦 = 3 1 , π‘₯ = 5 9
  • D 𝑦 = 3 1 , π‘₯ = 9 0

Q3:

Find π‘₯ and 𝑦 .

  • A π‘₯ = 3 3 , 𝑦 = 5 7
  • B π‘₯ = 5 7 , 𝑦 = 3 3
  • C π‘₯ = 1 1 4 , 𝑦 = 6 6
  • D π‘₯ = 6 6 , 𝑦 = 1 1 4

Q4:

Given that π‘š ∠ 𝐷 𝐴 𝐡 = 5 8 ∘ , find π‘š ∠ 𝐢 𝐴 𝐡 .

  • A 3 3 ∘
  • B 2 9 ∘
  • C 6 5 ∘
  • D 7 ∘

Q5:

Given that 𝐴 𝑀 = 5 0 c m , find the length of 𝐡 𝐢 .

Q6:

Given that ∠ 𝐴 𝐡 𝐷 = 3 3 ∘ and ∠ 𝐢 𝐸 𝐡 = 6 7 ∘ , find ∠ 𝐢 𝐴 𝐡 and ∠ 𝐷 𝐴 𝐢 .

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

Q7:

Find π‘š ∠ 𝐢 𝑀 𝐷 .

Q8:

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

Q9:

Given that π‘š ∠ 𝐡 𝐸 𝐷 = ( 3 π‘₯ βˆ’ 1 8 ) ∘ , find π‘₯ .

Q10:

Point 𝐴 is outside a circle centre 𝑀 , and  𝐴 𝑀 meets the circle in 𝐢 and 𝐷 . Suppose that  𝐴 𝐡 is tangent to the circle at 𝐡 and ∠ 𝐴 = 9 ∘ . What is ∠ 𝐡 𝐷 𝐢 ?

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 π‘š ∠ 𝐢 𝑀 𝐷 .

Q13:

Given that π‘š ∠ 𝐷 𝐴 𝐡 = 8 4 ∘ , find π‘š ∠ 𝐢 𝐴 𝐡 .

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

Q14:

Given that π‘š ∠ 𝐷 𝐴 𝐡 = 7 6 ∘ , find π‘š ∠ 𝐢 𝐴 𝐡 .

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

Q15:

Given that ∠ 𝐴 𝐡 𝐷 = 3 2 ∘ and ∠ 𝐢 𝐸 𝐡 = 6 3 ∘ , find ∠ 𝐢 𝐴 𝐡 and ∠ 𝐷 𝐴 𝐢 .

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