Worksheet: Sum of Angles of a Triangle

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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