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Worksheet: Applications of Angles in a Semicircle

Q1:

Find .

  • A
  • B
  • C
  • D

Q2:

Given that , find and .

  • A ,
  • B ,
  • C ,
  • D ,

Q3:

Find π‘₯ and 𝑦 .

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

Q4:

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

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

Q5:

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

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

Q6:

Given that , find .

  • A
  • B
  • C
  • D

Q7:

Given that , find .

  • A
  • B
  • C
  • D

Q8:

Given that , find .

  • A
  • B
  • C
  • D

Q9:

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

Q10:

Find π‘š ∠ 𝐢 𝑀 𝐷 .

Q11:

Find π‘š ∠ 𝐢 𝑀 𝐷 .

Q12:

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 .

Q13:

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

Q14:

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

  • A 9 ∘
  • B 8 1 ∘
  • C 1 8 ∘
  • D 4 0 . 5 ∘

Q15:

In the given figure, 𝐴 𝐡 is a diameter.

What is the measure of angle 𝐴 𝐢 𝐡 ?

Given that the measure of angle 𝐴 𝐡 𝐢 = 3 7 ∘ , find the measure of angle 𝐡 𝐴 𝐢 .

Calculate the measure of angle 𝐴 𝑂 𝐢 .