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Lesson: Sum of Interior Angles of Quadrilaterals

Sample Question Videos

Worksheet • 24 Questions • 1 Video

Q1:

𝐴 𝐡 𝐢 𝐷 is a quadrilateral where π‘š ∠ 𝐴 = 1 6 5 ∘ , π‘š ∠ 𝐴 𝐡 𝐢 = 4 π‘₯ ∘ , π‘š ∠ 𝐡 𝐢 𝐷 = 4 π‘₯ ∘ , and π‘š ∠ 𝐢 𝐷 𝐴 = 5 π‘₯ ∘ . What is π‘₯ ?

Q2:

In the given figure, π‘š ∠ 𝐴 = 7 4 ∘ and π‘š ∠ 𝐢 = 9 2 ∘ . Find π‘š ∠ 𝐷 .

Q3:

Determine the value of π‘₯ in the given quadrilateral.

Q4:

Find .

  • A
  • B
  • C
  • D
  • E

Q5:

In a quadrilateral , if , find .

Q6:

The sum of the sizes of the angles of a trapezium is . Write an equation to find the missing size , and then solve it.

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q7:

From the figure, in which π‘š ∠ 𝐢 𝐷 𝐴 = 5 π‘₯ ∘ , π‘š ∠ 𝐡 𝐢 𝐷 = 7 𝑦 ∘ , and π‘š ∠ 𝐴 𝐡 𝐢 = 8 𝑦 ∘ , find the values of π‘₯ and 𝑦 .

  • A π‘₯ = 1 9 , 𝑦 = 1 2
  • B π‘₯ = 9 5 , 𝑦 = 1 2
  • C π‘₯ = 1 9 , 𝑦 = 9 5
  • D π‘₯ = 9 5 , 𝑦 = 8 4

Q8:

Given that π‘š ∠ 𝐷 = 2 3 π‘š ∠ 𝐡 , find π‘š ∠ 𝐡 and π‘š ∠ 𝐷 .

  • A π‘š ∠ 𝐡 = 1 0 8 ∘ , π‘š ∠ 𝐷 = 7 2 ∘
  • B π‘š ∠ 𝐡 = 7 2 ∘ , π‘š ∠ 𝐷 = 1 0 8 ∘
  • C π‘š ∠ 𝐡 = 1 2 7 ∘ , π‘š ∠ 𝐷 = 5 3 ∘
  • D π‘š ∠ 𝐡 = 5 3 ∘ , π‘š ∠ 𝐷 = 1 2 7 ∘

Q9:

Determine π‘š ∠ 𝐢 𝐴 𝐡 .

Q10:

From the figure, determine π‘š ∠ 𝐡 𝐸 𝐷 .

  • A 4 2 ∘
  • B 9 0 ∘
  • C 8 0 ∘
  • D 2 2 ∘
  • E 3 2 ∘

Q11:

In the figure, π‘š ∠ 𝐴 = 3 4 ∘ , π‘š ∠ 𝐹 = 4 8 ∘ , and π‘š ∠ 𝐡 𝐸 𝐹 = 3 4 ∘ . Determine the measure of all angles in 𝐷 𝐸 𝐡 𝐢 .

  • A π‘š ∠ 𝐸 𝐡 𝐢 = 8 2 ∘ , π‘š ∠ 𝐢 = 6 4 ∘ , π‘š ∠ 𝐡 𝐸 𝐷 = 1 4 6 ∘ , π‘š ∠ 𝐸 𝐷 𝐢 = 6 8 ∘
  • B π‘š ∠ 𝐸 𝐡 𝐢 = 8 2 ∘ , π‘š ∠ 𝐢 = 9 8 ∘ , π‘š ∠ 𝐡 𝐸 𝐷 = 3 4 ∘ , π‘š ∠ 𝐸 𝐷 𝐢 = 1 4 6 ∘
  • C π‘š ∠ 𝐸 𝐡 𝐢 = 6 4 ∘ , π‘š ∠ 𝐢 = 8 2 ∘ , π‘š ∠ 𝐡 𝐸 𝐷 = 1 1 6 ∘ , π‘š ∠ 𝐸 𝐷 𝐢 = 9 8 ∘
  • D π‘š ∠ 𝐸 𝐡 𝐢 = 4 8 ∘ , π‘š ∠ 𝐢 = 6 4 ∘ , π‘š ∠ 𝐡 𝐸 𝐷 = 3 4 ∘ , π‘š ∠ 𝐸 𝐷 𝐢 = 2 1 4 ∘

Q12:

Determine π‘š ∠ 𝐹 𝐸 𝐢 .

Q13:

In the figure, if π‘š ∠ 𝐴 = 2 6 ∘ , π‘š ∠ 𝐴 𝐢 𝐡 = 5 4 ∘ , π‘š ∠ 𝐹 = 1 4 6 ∘ , determine π‘š ∠ 𝐸 .

Q14:

The internal angles of a quadrilateral are in the ratio 3 ∢ 4 ∢ 5 ∢ 6 . What is the largest angle?

  • A 1 2 0 ∘
  • B 2 0 ∘
  • C 8 0 ∘
  • D 6 0 ∘

Q15:

In the given figure, find and .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q16:

Find the sizes of the angles of a quadrilateral given that the ratio between them is .

  • A , , ,
  • B , , ,
  • C , , ,
  • D , , ,
  • E , , ,

Q17:

𝐴 𝐡 𝐢 𝐷 is a quadrilateral where π‘š ∠ 𝐴 = 1 6 2 ∘ , π‘š ∠ 𝐴 𝐡 𝐢 = 4 π‘₯ ∘ , π‘š ∠ 𝐡 𝐢 𝐷 = 2 π‘₯ ∘ , and π‘š ∠ 𝐢 𝐷 𝐴 = 3 π‘₯ ∘ . What is π‘₯ ?

Q18:

Find .

  • A
  • B
  • C
  • D

Q19:

Find .

  • A
  • B
  • C
  • D
  • E

Q20:

Determine the value of π‘₯ in the given quadrilateral.

Q21:

Determine the value of π‘₯ in the given quadrilateral.

Q22:

In a quadrilateral , if , find .

Q23:

In the given figure, π‘š ∠ 𝐴 = 6 0 ∘ and π‘š ∠ 𝐢 = 1 1 8 ∘ . Find π‘š ∠ 𝐷 .

Q24:

In the given figure, π‘š ∠ 𝐴 = 7 5 ∘ and π‘š ∠ 𝐢 = 9 6 ∘ . Find π‘š ∠ 𝐷 .

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