Worksheet: The Sum of Angles in Quadrilaterals

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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:

𝐴𝐵𝐶𝐷 is a quadrilateral where 𝑚∠𝐴=165∘, 𝑚∠𝐴𝐵𝐶=4𝑥∘, 𝑚∠𝐵𝐶𝐷=4𝑥∘, and 𝑚∠𝐶𝐷𝐴=5𝑥∘. What is 𝑥?

Q2:

In the given figure, 𝑚∠𝐴=74∘ and 𝑚∠𝐶=92∘. Find 𝑚∠𝐷.

Q3:

Determine the value of 𝑥 in the given quadrilateral.

Q4:

Find 𝑚∠𝐴.

Q5:

In a quadrilateral𝐴𝐵𝐶𝐷, if 𝑚∠𝐴=3𝑚∠𝐵=3𝑚∠𝐶=72∘, find 𝑚∠𝐷.

Q6:

The sum of the measures of the angles of a trapezoid is 360∘. Write an equation to find the missing measure 𝑥, and then solve it.

  • A𝑥+102=180, 𝑥=78
  • B𝑥+102=180, 𝑥=102
  • C𝑥+102+116+78=360, 𝑥=64
  • D𝑥+102+116=360, 𝑥=102
  • E𝑥+102+116+78=360, 𝑥=78

Q7:

From the figure, in which 𝑚∠𝐶𝐷𝐴=5𝑥∘, 𝑚∠𝐵𝐶𝐷=7𝑦∘, and 𝑚∠𝐴𝐵𝐶=8𝑦∘, find the values of 𝑥 and 𝑦.

  • A𝑥=95, 𝑦=12
  • B𝑥=95, 𝑦=84
  • C𝑥=19, 𝑦=95
  • D𝑥=19, 𝑦=12

Q8:

Given that 𝑚∠𝐷=23𝑚∠𝐵, find 𝑚∠𝐵 and 𝑚∠𝐷.

  • A𝑚∠𝐵=108∘, 𝑚∠𝐷=72∘
  • B𝑚∠𝐵=53∘, 𝑚∠𝐷=127∘
  • C𝑚∠𝐵=72∘, 𝑚∠𝐷=108∘
  • D𝑚∠𝐵=127∘, 𝑚∠𝐷=53∘

Q9:

Determine 𝑚∠𝐶𝐴𝐵.

Q10:

From the figure, determine 𝑚∠𝐵𝐸𝐷.

Q11:

In the figure, 𝑚∠𝐴=34∘, 𝑚∠𝐹=48∘, and 𝑚∠𝐵𝐸𝐹=34∘. Determine the measure of all angles in 𝐷𝐸𝐵𝐶.

  • A𝑚∠𝐸𝐵𝐶=82∘, 𝑚∠𝐶=98∘, 𝑚∠𝐵𝐸𝐷=34∘, 𝑚∠𝐸𝐷𝐶=146∘
  • B𝑚∠𝐸𝐵𝐶=48∘, 𝑚∠𝐶=64∘, 𝑚∠𝐵𝐸𝐷=34∘, 𝑚∠𝐸𝐷𝐶=214∘
  • C𝑚∠𝐸𝐵𝐶=64∘, 𝑚∠𝐶=82∘, 𝑚∠𝐵𝐸𝐷=116∘, 𝑚∠𝐸𝐷𝐶=98∘
  • D𝑚∠𝐸𝐵𝐶=82∘, 𝑚∠𝐶=64∘, 𝑚∠𝐵𝐸𝐷=146∘, 𝑚∠𝐸𝐷𝐶=68∘

Q12:

Determine 𝑚∠𝐹𝐸𝐶.

Q13:

In the figure, if 𝑚∠𝐴=26∘, 𝑚∠𝐴𝐶𝐵=54∘, 𝑚∠𝐹=146∘, determine 𝑚∠𝐸.

Q14:

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

Q15:

In the given figure, find 𝑥 and 𝑦.

  • A𝑥=16, 𝑦=31
  • B𝑥=14, 𝑦=31
  • C𝑥=19, 𝑦=48
  • D𝑥=16, 𝑦=59
  • E𝑥=96, 𝑦=118

Q16:

Find the measures of the angles of a quadrilateral given that the ratio between them is 691213:::.

  • A87∘, 81∘, 93∘, 99∘
  • B63∘, 117∘, 54∘, 126∘
  • C22∘, 28∘, 37∘, 49∘
  • D15∘, 18∘, 21∘, 22∘
  • E54∘, 81∘, 108∘, 117∘

Q17:

𝐴𝐵𝐶𝐷 is a quadrilateral where 𝑚∠𝐴=162∘, 𝑚∠𝐴𝐵𝐶=4𝑥∘, 𝑚∠𝐵𝐶𝐷=2𝑥∘, and 𝑚∠𝐶𝐷𝐴=3𝑥∘. What is 𝑥?

Q18:

Find 𝑚∠𝐴.

Q19:

Find 𝑚∠𝐴.

Q20:

Determine the value of 𝑥 in the given quadrilateral.

Q21:

Determine the value of 𝑥 in the given quadrilateral.

Q22:

In a quadrilateral𝐴𝐵𝐶𝐷, if 𝑚∠𝐴=9𝑚∠𝐵=5𝑚∠𝐶=45∘, find 𝑚∠𝐷.

Q23:

In the given figure, 𝑚∠𝐴=60∘ and 𝑚∠𝐶=118∘. Find 𝑚∠𝐷.

Q24:

In the given figure, 𝑚∠𝐴=75∘ and 𝑚∠𝐶=96∘. Find 𝑚∠𝐷.

Q25:

Three angles in a quadrilateral are 156 rad, 215 rad and 31∘. Find the measure of the fourth angle in radians giving the answer to three decimal places.

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