Worksheet: The Sum of Angles in 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:

𝐴 𝐵 𝐶 𝐷 is a quadrilateral where 𝑚𝐴=165, 𝑚𝐴𝐵𝐶=4𝑥, 𝑚𝐵𝐶𝐷=4𝑥, and 𝑚𝐶𝐷𝐴=5𝑥. What is 𝑥?

Q2:

In the given figure, 𝑚𝐴=74 and 𝑚𝐶=92. Find 𝑚𝐷.

Q3:

Determine the value of 𝑥 in the given quadrilateral.

Q4:

Find 𝑚𝐴.

Q5:

In a quadrilateral𝐴𝐵𝐶𝐷, if 𝑚𝐴=3𝑚𝐵=3𝑚𝐶=72, find 𝑚𝐷.

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.

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

Q7:

From the figure, in which 𝑚𝐶𝐷𝐴=5𝑥, 𝑚𝐵𝐶𝐷=7𝑦, and 𝑚𝐴𝐵𝐶=8𝑦, find the values of 𝑥 and 𝑦.

  • A 𝑥 = 9 5 , 𝑦 = 8 4
  • B 𝑥 = 9 5 , 𝑦 = 1 2
  • C 𝑥 = 1 9 , 𝑦 = 1 2
  • D 𝑥 = 1 9 , 𝑦 = 9 5

Q8:

Given that 𝑚𝐷=23𝑚𝐵, find 𝑚𝐵 and 𝑚𝐷.

  • A 𝑚 𝐵 = 1 0 8 , 𝑚 𝐷 = 7 2
  • B 𝑚 𝐵 = 5 3 , 𝑚 𝐷 = 1 2 7
  • C 𝑚 𝐵 = 7 2 , 𝑚 𝐷 = 1 0 8
  • D 𝑚 𝐵 = 1 2 7 , 𝑚 𝐷 = 5 3

Q9:

Determine 𝑚𝐶𝐴𝐵.

Q10:

From the figure, determine 𝑚𝐵𝐸𝐷.

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

Q11:

In the figure, 𝑚𝐴=34, 𝑚𝐹=48, and 𝑚𝐵𝐸𝐹=34. Determine the measure of all angles in 𝐷𝐸𝐵𝐶.

  • A 𝑚 𝐸 𝐵 𝐶 = 8 2 , 𝑚 𝐶 = 9 8 , 𝑚 𝐵 𝐸 𝐷 = 3 4 , 𝑚 𝐸 𝐷 𝐶 = 1 4 6
  • B 𝑚 𝐸 𝐵 𝐶 = 4 8 , 𝑚 𝐶 = 6 4 , 𝑚 𝐵 𝐸 𝐷 = 3 4 , 𝑚 𝐸 𝐷 𝐶 = 2 1 4
  • C 𝑚 𝐸 𝐵 𝐶 = 6 4 , 𝑚 𝐶 = 8 2 , 𝑚 𝐵 𝐸 𝐷 = 1 1 6 , 𝑚 𝐸 𝐷 𝐶 = 9 8
  • D 𝑚 𝐸 𝐵 𝐶 = 8 2 , 𝑚 𝐶 = 6 4 , 𝑚 𝐵 𝐸 𝐷 = 1 4 6 , 𝑚 𝐸 𝐷 𝐶 = 6 8

Q12:

Determine 𝑚𝐹𝐸𝐶.

Q13:

In the figure, if 𝑚𝐴=26, 𝑚𝐴𝐶𝐵=54, 𝑚𝐹=146, determine 𝑚𝐸.

Q14:

The internal angles of a quadrilateral are in the ratio 3456. What is the largest angle?

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

Q15:

In the given figure, find 𝑥 and 𝑦.

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

Q16:

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

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

Q17:

𝐴 𝐵 𝐶 𝐷 is a quadrilateral where 𝑚𝐴=162, 𝑚𝐴𝐵𝐶=4𝑥, 𝑚𝐵𝐶𝐷=2𝑥, and 𝑚𝐶𝐷𝐴=3𝑥. What is 𝑥?

Q18:

Find 𝑚𝐴.

Q19:

Find 𝑚𝐴.

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 𝑚𝐴=9𝑚𝐵=5𝑚𝐶=45, find 𝑚𝐷.

Q23:

In the given figure, 𝑚𝐴=60 and 𝑚𝐶=118. Find 𝑚𝐷.

Q24:

In the given figure, 𝑚𝐴=75 and 𝑚𝐶=96. Find 𝑚𝐷.

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.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.