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Worksheet: Triangle Angle Sum Theorem

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 π‘Œ 𝑍 , we have π‘š ∠ 𝑋 = 3 0 ∘ and π‘š ∠ π‘Œ = π‘š ∠ 𝑍 . What is π‘š ∠ 𝑍 ?

Q2:

The measures of the base angles of an isosceles triangle are ( 9 π‘š βˆ’ 2 𝑛 ) ∘ and ( 5 π‘š + 2 𝑛 ) ∘ , and the measure of the vertex angle is ( 4 π‘š ) ∘ . Find the values of π‘š and 𝑛 .

  • A π‘š = 1 0 , 𝑛 = 2 0
  • B π‘š = 1 3 , 𝑛 = 1 3
  • C π‘š = 1 3 , 𝑛 = 2 6
  • D π‘š = 1 0 , 𝑛 = 1 0

Q3:

Find the size of .

  • A
  • B
  • C
  • D

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 greater than
  • B less than
  • C equal to

Q6:

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

Q7:

Calculate the value of π‘₯ .

Q8:

In triangle 𝐴 𝐡 𝐢 , π‘š ∠ 𝐴 = 7 8 ∘ and π‘š ∠ 𝐡 = 2 π‘š ∠ 𝐢 . What is π‘š ∠ 𝐢 ?

Q9:

Find π‘š ∠ 𝐴 𝐡 𝐢 .

Q10:

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

  • A , ,
  • B , ,
  • C , ,
  • D , ,

Q11:

In triangle 𝐴 𝐡 𝐢 , the measures of angles in degrees at 𝐴 , 𝐡 , and 𝐢 are 2 π‘₯ , ( 3 π‘₯ + 7 ) , and 43, respectively. Find π‘š ∠ 𝐴 and π‘š ∠ 𝐡 .

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

Q12:

Determine the values of and .

  • A ,
  • B ,
  • C ,
  • D ,

Q13:

In triangle 𝐴 𝐡 𝐢 , π‘š ∠ 𝐴 = 5 4 ∘ and π‘š ∠ 𝐡 = 7 1 ∘ . Find π‘š ∠ 𝐢 .

Q14:

In β–³ 𝐴 𝐡 𝐢 , π‘š ∠ 𝐡 = 2 π‘š ∠ 𝐴 = 4 0 ∘ . Determine π‘š ∠ 𝐢 .

Q15:

In the figure below, given that 𝐴 𝐡 𝐢 𝐷 is a rectangle, determine π‘š ∠ 𝐢 𝐷 𝐸 .

Q16:

If 𝐴 𝐡 𝐢 is a triangle in which π‘š ∠ 𝐴 = 7 9 π‘š ∠ 𝐡 and π‘š ∠ 𝐢 = 2 π‘š ∠ 𝐴 . Calculate the measures of angles 𝐴 , 𝐡 , and 𝐢 .

  • A π‘š ∠ 𝐴 = 3 7 ∘ , π‘š ∠ 𝐡 = 4 8 ∘ , π‘š ∠ 𝐢 = 9 5 ∘
  • B π‘š ∠ 𝐴 = 7 0 ∘ , π‘š ∠ 𝐡 = 9 0 ∘ , π‘š ∠ 𝐢 = 2 0 ∘
  • C π‘š ∠ 𝐴 = 7 6 ∘ , π‘š ∠ 𝐡 = 8 5 ∘ , π‘š ∠ 𝐢 = 1 9 ∘
  • D π‘š ∠ 𝐴 = 4 2 ∘ , π‘š ∠ 𝐡 = 5 4 ∘ , π‘š ∠ 𝐢 = 8 4 ∘

Q17:

In the triangle 𝐴 𝐡 𝐢 , π‘š ∠ 𝐴 = ο€Ή π‘₯ + 9 7  2 ∘ , π‘š ∠ 𝐡 = ( 6 0 βˆ’ 5 π‘₯ ) ∘ , and π‘š ∠ 𝐢 = ( 5 9 βˆ’ 7 π‘₯ ) ∘ . Find the measure of each angle.

  • A π‘š ∠ 𝐴 = 1 5 7 ∘ , π‘š ∠ 𝐡 = 2 0 ∘ , π‘š ∠ 𝐢 = 3 ∘
  • B π‘š ∠ 𝐴 = 1 3 3 ∘ , π‘š ∠ 𝐡 = 2 5 ∘ , π‘š ∠ 𝐢 = 2 2 ∘
  • C π‘š ∠ 𝐴 = 1 2 2 ∘ , π‘š ∠ 𝐡 = 3 5 ∘ , π‘š ∠ 𝐢 = 2 4 ∘
  • D π‘š ∠ 𝐴 = 1 3 3 ∘ , π‘š ∠ 𝐡 = 3 0 ∘ , π‘š ∠ 𝐢 = 1 7 ∘
  • E π‘š ∠ 𝐴 = 1 3 3 ∘ , π‘š ∠ 𝐡 = 3 0 ∘ , π‘š ∠ 𝐢 = 2 0 ∘

Q18:

Given that 𝐴 𝐡 𝐢 is a triangle in which π‘š ∠ 𝐴 = ( 2 π‘₯ + 6 ) ∘ , π‘š ∠ 𝐡 = ( 3 π‘₯ + 3 ) ∘ , and π‘š ∠ 𝐢 = ( 5 π‘₯ + 6 ) ∘ , determine π‘š ∠ 𝐴 .

Q19:

Find the measure of each angle in the triangle below.

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

Q20:

The figure shows a rectangle 𝐴 𝐡 𝐢 𝐷 and a square 𝐴 𝐡 π‘Œ 𝑋 . What is π‘š ∠ 𝐴 π‘Œ 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 , . If is an altitude of , find .

  • A37.8
  • B16.2
  • C34.2
  • D19.8
  • E18

Q23:

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

  • A , ,
  • B , ,
  • C , ,
  • D , ,
  • E , ,

Q24:

Suppose that in the figure, π‘š ∠ 𝐿 = 2 π‘₯ ∘ and π‘š ∠ 𝐾 = 4 π‘₯ ∘ . Determine these two angles.

  • A π‘š ∠ 𝐿 = 6 0 ∘ , π‘š ∠ 𝐾 = 1 2 0 ∘
  • B π‘š ∠ 𝐿 = 6 0 ∘ , π‘š ∠ 𝐾 = 3 0 ∘
  • C π‘š ∠ 𝐿 = 1 2 0 ∘ , π‘š ∠ 𝐾 = 6 0 ∘
  • D π‘š ∠ 𝐿 = 3 0 ∘ , π‘š ∠ 𝐾 = 6 0 ∘
  • E π‘š ∠ 𝐿 = 3 0 ∘ , π‘š ∠ 𝐾 = 1 2 0 ∘

Q25:

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

  • A , ,
  • B , ,
  • C , ,
  • D , ,
  • E , ,

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