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Worksheet: Sum of Interior Angles of Quadrilaterals

In this worksheet, we will practice finding a missing angle's measure in a quadrilateral knowing that the sum of angles in a quadrilateral is 360 degrees.

Q1:

is a quadrilateral where , , , and . What is ?

  • A189
  • B198
  • C4
  • D22

Q2:

is a quadrilateral where , , , and . What is ?

  • A182
  • B195
  • C27.7
  • D15

Q3:

Find 𝑚 ∠ 𝐴 .

Q4:

Find 𝑚 ∠ 𝐴 .

Q5:

Find 𝑚 ∠ 𝐴 .

Q6:

Find the measures of the angles of a quadrilateral given that the ratio between them is 6 9 1 2 1 3 : : : .

  • A 6 3 ∘ , 1 1 7 ∘ , 5 4 ∘ , 1 2 6 ∘
  • B 1 5 ∘ , 1 8 ∘ , 2 1 ∘ , 2 2 ∘
  • C 8 7 ∘ , 8 1 ∘ , 9 3 ∘ , 9 9 ∘
  • D 5 4 ∘ , 8 1 ∘ , 1 0 8 ∘ , 1 1 7 ∘
  • E 2 2 ∘ , 2 8 ∘ , 3 7 ∘ , 4 9 ∘

Q7:

Given that , find and .

  • A ,
  • B ,
  • C ,
  • D ,

Q8:

Determine .

  • A
  • B
  • C

Q9:

From the figure, determine .

  • A
  • B
  • C
  • D
  • E

Q10:

Determine the value of 𝑥 in the given quadrilateral.

Q11:

Determine the value of 𝑥 in the given quadrilateral.

Q12:

Determine the value of 𝑥 in the given quadrilateral.

Q13:

The sum of the measures of the angles of a trapezoid is 3 6 0 ∘ . Write an equation to find the missing measure 𝑥 , and then solve it.

  • A 𝑥 + 1 0 2 = 1 8 0 , 𝑥 = 7 8
  • B 𝑥 + 1 0 2 + 1 1 6 = 3 6 0 , 𝑥 = 1 0 2
  • C 𝑥 + 1 0 2 + 1 1 6 + 7 8 = 3 6 0 , 𝑥 = 7 8
  • D 𝑥 + 1 0 2 + 1 1 6 + 7 8 = 3 6 0 , 𝑥 = 6 4
  • E 𝑥 + 1 0 2 = 1 8 0 , 𝑥 = 1 0 2

Q14:

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

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

Q15:

In the figure, , , and . Determine the size of all angles in .

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

Q16:

In a quadrilateral , if , find .

  • A
  • B
  • C
  • D

Q17:

In a quadrilateral , if , find .

  • A
  • B
  • C
  • D

Q18:

Determine 𝑚 ∠ 𝐹 𝐸 𝐶 .

Q19:

In the given figure, find 𝑥 and 𝑦 .

  • A 𝑥 = 1 9 , 𝑦 = 4 8
  • B 𝑥 = 9 6 , 𝑦 = 1 1 8
  • C 𝑥 = 1 6 , 𝑦 = 5 9
  • D 𝑥 = 1 6 , 𝑦 = 3 1
  • E 𝑥 = 1 4 , 𝑦 = 3 1

Q20:

In the figure, if , , , determine .

  • A
  • B
  • C
  • D

Q21:

From the figure, in which , , and , find the values of and .

  • A ,
  • B ,
  • C ,
  • D ,

Q22:

In the given figure, and . Find .

  • A
  • B
  • C
  • D

Q23:

In the given figure, and . Find .

  • A
  • B
  • C
  • D

Q24:

In the given figure, and . Find .

  • A
  • B
  • C
  • D

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