Worksheet: Angle Sum of a Triangle

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

Q1:

In triangle 𝑋𝑌𝑍, we have 𝑚∠𝑋=30∘ and 𝑚∠𝑌=𝑚∠𝑍. What is 𝑚∠𝑍?

Q2:

The measures of the base angles of an isosceles triangle are (9𝑚−2𝑛)∘ 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

Q3:

Find the measure of 𝑥.

Q4:

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

Q5:

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

Q6:

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

Q7:

Calculate the value of 𝑥.

Q8:

In triangle 𝐴𝐵𝐶, 𝑚∠𝐴=78∘ and 𝑚∠𝐵=2𝑚∠𝐶. What is 𝑚∠𝐶?

Q9:

Find 𝑚∠𝐴𝐵𝐶.

Q10:

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

Q11:

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

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

Q12:

Determine the values of 𝑥 and 𝑦.

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

Q13:

In triangle 𝐴𝐵𝐶, 𝑚∠𝐴=54∘ and 𝑚∠𝐵=71∘. Find 𝑚∠𝐶.

Q14:

In △𝐴𝐵𝐶, 𝑚∠𝐵=2𝑚∠𝐴=40∘. Determine 𝑚∠𝐶.

Q15:

In the figure below, given that 𝐴𝐵𝐶𝐷 is a rectangle, determine 𝑚∠𝐶𝐷𝐸.

Q16:

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

  • A𝑚∠𝐴=37∘, 𝑚∠𝐵=48∘, 𝑚∠𝐶=95∘
  • B𝑚∠𝐴=70∘, 𝑚∠𝐵=90∘, 𝑚∠𝐶=20∘
  • C𝑚∠𝐴=42∘, 𝑚∠𝐵=54∘, 𝑚∠𝐶=84∘
  • D𝑚∠𝐴=76∘, 𝑚∠𝐵=85∘, 𝑚∠𝐶=19∘

Q17:

In the triangle 𝐴𝐵𝐶, 𝑚∠𝐴=𝑥+97∘, 𝑚∠𝐵=(60−5𝑥)∘, and 𝑚∠𝐶=(59−7𝑥)∘. Find the measure of each angle.

  • A𝑚∠𝐴=133∘, 𝑚∠𝐵=30∘, 𝑚∠𝐶=20∘
  • B𝑚∠𝐴=133∘, 𝑚∠𝐵=30∘, 𝑚∠𝐶=17∘
  • C𝑚∠𝐴=133∘, 𝑚∠𝐵=25∘, 𝑚∠𝐶=22∘
  • D𝑚∠𝐴=157∘, 𝑚∠𝐵=20∘, 𝑚∠𝐶=3∘
  • E𝑚∠𝐴=122∘, 𝑚∠𝐵=35∘, 𝑚∠𝐶=24∘

Q18:

Given that 𝐴𝐵𝐶 is a triangle in which 𝑚∠𝐴=(2𝑥+6)∘, 𝑚∠𝐵=(3𝑥+3)∘, and 𝑚∠𝐶=(5𝑥+6)∘, determine 𝑚∠𝐴.

Q19:

Find the measure of each angle in the triangle below.

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

Q20:

The figure shows a rectangle 𝐴𝐵𝐶𝐷 and a square 𝐴𝐵𝑌𝑋. What is 𝑚∠𝐴𝑌𝐷?

Q21:

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?

Q22:

In △𝐽𝐿𝑃, 𝑚∠𝐽𝑀𝑃=(5𝑥−9)∘. If 𝐽𝑀 is an altitude of △𝐽𝐿𝑃, find 𝑥.

Q23:

If the ratio between the measures of the angles of a triangle is 11∶18∶7, determine the measures of the angles.

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

Q24:

Suppose that in the figure, 𝑚∠𝐿=2𝑥∘ and 𝑚∠𝐾=4𝑥∘. Determine these two angles.

  • A𝑚∠𝐿=30∘, 𝑚∠𝐾=120∘
  • B𝑚∠𝐿=30∘, 𝑚∠𝐾=60∘
  • C𝑚∠𝐿=60∘, 𝑚∠𝐾=120∘
  • D𝑚∠𝐿=60∘, 𝑚∠𝐾=30∘
  • E𝑚∠𝐿=120∘, 𝑚∠𝐾=60∘

Q25:

The measures of the angles in a triangle are in a ratio of 3∶2∶5. 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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