Worksheet: Angle Sum of a Triangle

In this worksheet, we will practice finding a missing angle in a triangle given the two other angles.


In triangle 𝑋𝑌𝑍, we have 𝑚𝑋=30 and 𝑚𝑌=𝑚𝑍. What is 𝑚𝑍?


The measures of the base angles of an isosceles triangle are (9𝑚2𝑛) and (5𝑚+2𝑛), and the measure of the vertex angle is (4𝑚). Find the values of 𝑚 and 𝑛.

  • A𝑚=10, 𝑛=10
  • B𝑚=13, 𝑛=13
  • C𝑚=10, 𝑛=20
  • D𝑚=13, 𝑛=26


Find the measure of 𝑥.


Complete the following: The sum of measures of the interior angles of a triangle is .


Complete the sentence: The measure of a straight angle is the sum of the measures of the interior angles of a triangle.

  • Agreater than
  • Bless than
  • Cequal to


What is the sum of the measures of the two acute angles in a right-angled triangle?


Calculate the value of 𝑥.


In triangle 𝐴𝐵𝐶, 𝑚𝐴=78 and 𝑚𝐵=2𝑚𝐶. What is 𝑚𝐶?


Find 𝑚𝐴𝐵𝐶.


The given design is carved on a wooden board. If 𝐶 is a right angle, determine the values of 𝑥, 𝑦, and 𝑧.

  • A𝑥=53, 𝑦=82, 𝑧=94
  • B𝑥=36, 𝑦=82, 𝑧=53
  • C𝑥=36, 𝑦=41, 𝑧=94
  • D𝑥=53, 𝑦=41, 𝑧=53


In triangle 𝐴𝐵𝐶, the measures of angles in degrees at 𝐴, 𝐵, and 𝐶 are 2𝑥, (3𝑥+7), and 43, respectively. Find 𝑚𝐴 and 𝑚𝐵.

  • A69.2, 67.8
  • B54.8, 82.2
  • C72, 65
  • D52, 85


Determine the values of 𝑥 and 𝑦.

  • A𝑥=90, 𝑦=90
  • B𝑥=47, 𝑦=43
  • C𝑥=43, 𝑦=47
  • D𝑥=137, 𝑦=133


In triangle 𝐴𝐵𝐶, 𝑚𝐴=54 and 𝑚𝐵=71. Find 𝑚𝐶.


In 𝐴𝐵𝐶, 𝑚𝐵=2𝑚𝐴=40. Determine 𝑚𝐶.


In the figure below, given that 𝐴𝐵𝐶𝐷 is a rectangle, determine 𝑚𝐶𝐷𝐸.


If 𝐴𝐵𝐶 is a triangle in which 𝑚𝐴=79𝑚𝐵 and 𝑚𝐶=2𝑚𝐴. Calculate the measures of angles 𝐴, 𝐵, and 𝐶.

  • A𝑚𝐴=37, 𝑚𝐵=48, 𝑚𝐶=95
  • B𝑚𝐴=70, 𝑚𝐵=90, 𝑚𝐶=20
  • C𝑚𝐴=42, 𝑚𝐵=54, 𝑚𝐶=84
  • D𝑚𝐴=76, 𝑚𝐵=85, 𝑚𝐶=19


In the triangle 𝐴𝐵𝐶, 𝑚𝐴=𝑥+97, 𝑚𝐵=(605𝑥), and 𝑚𝐶=(597𝑥). Find the measure of each angle.

  • A𝑚𝐴=133, 𝑚𝐵=30, 𝑚𝐶=20
  • B𝑚𝐴=133, 𝑚𝐵=30, 𝑚𝐶=17
  • C𝑚𝐴=133, 𝑚𝐵=25, 𝑚𝐶=22
  • D𝑚𝐴=157, 𝑚𝐵=20, 𝑚𝐶=3
  • E𝑚𝐴=122, 𝑚𝐵=35, 𝑚𝐶=24


Given that 𝐴𝐵𝐶 is a triangle in which 𝑚𝐴=(2𝑥+6), 𝑚𝐵=(3𝑥+3), and 𝑚𝐶=(5𝑥+6), determine 𝑚𝐴.


Find the measure of each angle in the triangle below.

  • A90, 47, 43
  • B90, 42, 48
  • C90, 45, 45
  • D90, 52, 38


The figure shows a rectangle 𝐴𝐵𝐶𝐷 and a square 𝐴𝐵𝑌𝑋. What is 𝑚𝐴𝑌𝐷?


The sum of the measures of the angles of a triangle is 180. In a right triangle, what is the sum of the measures of the two acute angles?


In 𝐽𝐿𝑃, 𝑚𝐽𝑀𝑃=(5𝑥9). If 𝐽𝑀 is an altitude of 𝐽𝐿𝑃, find 𝑥.


If the ratio between the measures of the angles of a triangle is 11187, determine the measures of the angles.

  • A55, 73, 62
  • B55, 90, 35
  • C16, 23, 12
  • D55, 60, 65
  • E35, 70, 105


Suppose that in the figure, 𝑚𝐿=2𝑥 and 𝑚𝐾=4𝑥. Determine these two angles.

  • A𝑚𝐿=30, 𝑚𝐾=120
  • B𝑚𝐿=30, 𝑚𝐾=60
  • C𝑚𝐿=60, 𝑚𝐾=120
  • D𝑚𝐿=60, 𝑚𝐾=30
  • E𝑚𝐿=120, 𝑚𝐾=60


The measures of the angles in a triangle are in a ratio of 325. Work out the measures of these angles.

  • A54, 36, 90
  • B30, 50, 100
  • C50, 78, 52
  • D54, 30, 96
  • E30, 20, 50

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