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:

𝐴𝐡𝐢𝐷 is a quadrilateral where π‘šβˆ π΄=165∘, π‘šβˆ π΄π΅πΆ=4π‘₯∘, π‘šβˆ π΅πΆπ·=4π‘₯∘, and π‘šβˆ πΆπ·π΄=5π‘₯∘. What is π‘₯?

Q2:

In the given figure, π‘šβˆ π΄=74∘ and π‘šβˆ πΆ=92∘. Find π‘šβˆ π·.

Q3:

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

Q4:

Find π‘šβˆ π΄.

Q5:

In a quadrilateral𝐴𝐡𝐢𝐷, if π‘šβˆ π΄=3π‘šβˆ π΅=3π‘šβˆ πΆ=72∘, find π‘šβˆ π·.

Q6:

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

  • Aπ‘₯+102=180, π‘₯=78
  • Bπ‘₯+102=180, π‘₯=102
  • Cπ‘₯+102+116+78=360, π‘₯=64
  • Dπ‘₯+102+116=360, π‘₯=102
  • Eπ‘₯+102+116+78=360, π‘₯=78

Q7:

From the figure, in which π‘šβˆ πΆπ·π΄=5π‘₯∘, π‘šβˆ π΅πΆπ·=7π‘¦βˆ˜, and π‘šβˆ π΄π΅πΆ=8π‘¦βˆ˜, find the values of π‘₯ and 𝑦.

  • Aπ‘₯=95, 𝑦=12
  • Bπ‘₯=95, 𝑦=84
  • Cπ‘₯=19, 𝑦=95
  • Dπ‘₯=19, 𝑦=12

Q8:

Given that π‘šβˆ π·=23π‘šβˆ π΅, find π‘šβˆ π΅ and π‘šβˆ π·.

  • Aπ‘šβˆ π΅=108∘, π‘šβˆ π·=72∘
  • Bπ‘šβˆ π΅=53∘, π‘šβˆ π·=127∘
  • Cπ‘šβˆ π΅=72∘, π‘šβˆ π·=108∘
  • Dπ‘šβˆ π΅=127∘, π‘šβˆ π·=53∘

Q9:

Determine π‘šβˆ πΆπ΄π΅.

Q10:

From the figure, determine π‘šβˆ π΅πΈπ·.

Q11:

In the figure, π‘šβˆ π΄=34∘, π‘šβˆ πΉ=48∘, and π‘šβˆ π΅πΈπΉ=34∘. Determine the measure of all angles in 𝐷𝐸𝐡𝐢.

  • Aπ‘šβˆ πΈπ΅πΆ=82∘, π‘šβˆ πΆ=98∘, π‘šβˆ π΅πΈπ·=34∘, π‘šβˆ πΈπ·πΆ=146∘
  • Bπ‘šβˆ πΈπ΅πΆ=48∘, π‘šβˆ πΆ=64∘, π‘šβˆ π΅πΈπ·=34∘, π‘šβˆ πΈπ·πΆ=214∘
  • Cπ‘šβˆ πΈπ΅πΆ=64∘, π‘šβˆ πΆ=82∘, π‘šβˆ π΅πΈπ·=116∘, π‘šβˆ πΈπ·πΆ=98∘
  • Dπ‘šβˆ πΈπ΅πΆ=82∘, π‘šβˆ πΆ=64∘, π‘šβˆ π΅πΈπ·=146∘, π‘šβˆ πΈπ·πΆ=68∘

Q12:

Determine π‘šβˆ πΉπΈπΆ.

Q13:

In the figure, if π‘šβˆ π΄=26∘, π‘šβˆ π΄πΆπ΅=54∘, π‘šβˆ πΉ=146∘, determine π‘šβˆ πΈ.

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 π‘₯ and 𝑦.

  • Aπ‘₯=16, 𝑦=31
  • Bπ‘₯=14, 𝑦=31
  • Cπ‘₯=19, 𝑦=48
  • Dπ‘₯=16, 𝑦=59
  • Eπ‘₯=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:

𝐴𝐡𝐢𝐷 is a quadrilateral where π‘šβˆ π΄=162∘, π‘šβˆ π΄π΅πΆ=4π‘₯∘, π‘šβˆ π΅πΆπ·=2π‘₯∘, and π‘šβˆ πΆπ·π΄=3π‘₯∘. What is π‘₯?

Q18:

Find π‘šβˆ π΄.

Q19:

Find π‘šβˆ π΄.

Q20:

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

Q21:

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

Q22:

In a quadrilateral𝐴𝐡𝐢𝐷, if π‘šβˆ π΄=9π‘šβˆ π΅=5π‘šβˆ πΆ=45∘, find π‘šβˆ π·.

Q23:

In the given figure, π‘šβˆ π΄=60∘ and π‘šβˆ πΆ=118∘. Find π‘šβˆ π·.

Q24:

In the given figure, π‘šβˆ π΄=75∘ and π‘šβˆ πΆ=96∘. Find π‘šβˆ π·.

Q25:

Three angles in a quadrilateral are ο€Ό156 rad, ο€Ό215 rad and 31∘. Find the measure of the fourth angle in radians giving the answer to three decimal places.

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