Worksheet: Sum of Angles of a Triangle

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

Q1:

In triangle 𝑋 𝑌 𝑍 , we have 𝑚 ∠ 𝑋 = 3 0 ∘ and 𝑚 ∠ 𝑌 = 𝑚 ∠ 𝑍 . What is 𝑚 ∠ 𝑍 ?

Q2:

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

  • A 𝑚 = 1 3 , 𝑛 = 1 3
  • B 𝑚 = 1 0 , 𝑛 = 2 0
  • C 𝑚 = 1 0 , 𝑛 = 1 0
  • D 𝑚 = 1 3 , 𝑛 = 2 6

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.

  • A less than
  • B equal to
  • C greater than

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 𝐴 𝐵 𝐶 , 𝑚 ∠ 𝐴 = 7 8 ∘ and 𝑚 ∠ 𝐵 = 2 𝑚 ∠ 𝐶 . What is 𝑚 ∠ 𝐶 ?

Q9:

Find 𝑚 ∠ 𝐴 𝐵 𝐶 .

Q10:

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

  • A 𝑥 = 3 6 , 𝑦 = 8 2 , 𝑧 = 5 3
  • B 𝑥 = 5 3 , 𝑦 = 8 2 , 𝑧 = 9 4
  • C 𝑥 = 3 6 , 𝑦 = 4 1 , 𝑧 = 9 4
  • D 𝑥 = 5 3 , 𝑦 = 4 1 , 𝑧 = 5 3

Q11:

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

  • A 6 9 . 2 ∘ , 6 7 . 8 ∘
  • B 7 2 ∘ , 6 5 ∘
  • C 5 4 . 8 ∘ , 8 2 . 2 ∘
  • D 5 2 ∘ , 8 5 ∘

Q12:

Determine the values of 𝑥 and 𝑦 .

  • A 𝑥 = 9 0 , 𝑦 = 9 0
  • B 𝑥 = 4 7 , 𝑦 = 4 3
  • C 𝑥 = 4 3 , 𝑦 = 4 7
  • D 𝑥 = 1 3 7 , 𝑦 = 1 3 3

Q13:

In triangle 𝐴 𝐵 𝐶 , 𝑚 ∠ 𝐴 = 5 4 ∘ and 𝑚 ∠ 𝐵 = 7 1 ∘ . Find 𝑚 ∠ 𝐶 .

Q14:

In △ 𝐴 𝐵 𝐶 , 𝑚 ∠ 𝐵 = 2 𝑚 ∠ 𝐴 = 4 0 ∘ . Determine 𝑚 ∠ 𝐶 .

Q15:

In the figure below, given that 𝐴 𝐵 𝐶 𝐷 is a rectangle, determine 𝑚 ∠ 𝐶 𝐷 𝐸 .

Q16:

If 𝐴 𝐵 𝐶 is a triangle in which 𝑚 ∠ 𝐴 = 7 9 𝑚 ∠ 𝐵 and 𝑚 ∠ 𝐶 = 2 𝑚 ∠ 𝐴 . Calculate the measures of angles 𝐴 , 𝐵 , and 𝐶 .

  • A 𝑚 ∠ 𝐴 = 7 0 ∘ , 𝑚 ∠ 𝐵 = 9 0 ∘ , 𝑚 ∠ 𝐶 = 2 0 ∘
  • B 𝑚 ∠ 𝐴 = 7 6 ∘ , 𝑚 ∠ 𝐵 = 8 5 ∘ , 𝑚 ∠ 𝐶 = 1 9 ∘
  • C 𝑚 ∠ 𝐴 = 3 7 ∘ , 𝑚 ∠ 𝐵 = 4 8 ∘ , 𝑚 ∠ 𝐶 = 9 5 ∘
  • D 𝑚 ∠ 𝐴 = 4 2 ∘ , 𝑚 ∠ 𝐵 = 5 4 ∘ , 𝑚 ∠ 𝐶 = 8 4 ∘

Q17:

In the triangle 𝐴 𝐵 𝐶 , 𝑚 ∠ 𝐴 = 𝑥 + 9 7 ∘ , 𝑚 ∠ 𝐵 = ( 6 0 − 5 𝑥 ) ∘ , and 𝑚 ∠ 𝐶 = ( 5 9 − 7 𝑥 ) ∘ . Find the measure of each angle.

  • A 𝑚 ∠ 𝐴 = 1 3 3 ∘ , 𝑚 ∠ 𝐵 = 3 0 ∘ , 𝑚 ∠ 𝐶 = 1 7 ∘
  • B 𝑚 ∠ 𝐴 = 1 2 2 ∘ , 𝑚 ∠ 𝐵 = 3 5 ∘ , 𝑚 ∠ 𝐶 = 2 4 ∘
  • C 𝑚 ∠ 𝐴 = 1 3 3 ∘ , 𝑚 ∠ 𝐵 = 2 5 ∘ , 𝑚 ∠ 𝐶 = 2 2 ∘
  • D 𝑚 ∠ 𝐴 = 1 5 7 ∘ , 𝑚 ∠ 𝐵 = 2 0 ∘ , 𝑚 ∠ 𝐶 = 3 ∘
  • E 𝑚 ∠ 𝐴 = 1 3 3 ∘ , 𝑚 ∠ 𝐵 = 3 0 ∘ , 𝑚 ∠ 𝐶 = 2 0 ∘

Q18:

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

Q19:

Find the measure of each angle in the triangle below.

  • A 9 0 ∘ , 4 5 ∘ , 4 5 ∘
  • B 9 0 ∘ , 4 2 ∘ , 4 8 ∘
  • C 9 0 ∘ , 5 2 ∘ , 3 8 ∘
  • D 9 0 ∘ , 4 7 ∘ , 4 3 ∘

Q20:

The figure shows a rectangle 𝐴 𝐵 𝐶 𝐷 and a square 𝐴 𝐵 𝑌 𝑋 . What is 𝑚 ∠ 𝐴 𝑌 𝐷 ?

Q21:

The sum of the measures of the angles of a triangle is 1 8 0 ∘ . In a right triangle, what is the sum of the measures of the two acute angles?

Q22:

In △ 𝐽 𝐿 𝑃 , 𝑚 ∠ 𝐽 𝑀 𝑃 = ( 5 𝑥 − 9 ) ∘ . If 𝐽 𝑀 is an altitude of △ 𝐽 𝐿 𝑃 , find 𝑥 .

Q23:

If the ratio between the measures of the angles of a triangle is 1 1 ∶ 1 8 ∶ 7 , determine the measures of the angles.

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

Q24:

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

  • A 𝑚 ∠ 𝐿 = 3 0 ∘ , 𝑚 ∠ 𝐾 = 6 0 ∘
  • B 𝑚 ∠ 𝐿 = 6 0 ∘ , 𝑚 ∠ 𝐾 = 3 0 ∘
  • C 𝑚 ∠ 𝐿 = 1 2 0 ∘ , 𝑚 ∠ 𝐾 = 6 0 ∘
  • D 𝑚 ∠ 𝐿 = 3 0 ∘ , 𝑚 ∠ 𝐾 = 1 2 0 ∘
  • E 𝑚 ∠ 𝐿 = 6 0 ∘ , 𝑚 ∠ 𝐾 = 1 2 0 ∘

Q25:

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

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

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