Worksheet: Types of Triangles According to Their Angles

In this worksheet, we will practice determining the type of a triangle according to its angles.

Q1:

If π‘š ∠ 𝐴 = 5 6 ∘ , π‘š ∠ 𝐡 = 6 6 ∘ , and π‘š ∠ 𝐢 = 5 8 ∘ , what is the type of β–³ 𝐴 𝐡 𝐢 in terms of the measures of its angles?

  • Aobtuse-angled triangle
  • Bright-angled triangle
  • Cacute-angled triangle

Q2:

Given that 𝐴 𝐡 𝐢 is a triangle in which π‘š ∠ 𝐴 ∢ π‘š ∠ 𝐡 ∢ π‘š ∠ 𝐢 = 4 ∢ 5 ∢ 6 , determine the triangle’s type in terms of its angles without finding their measures.

  • Aobtuse-angled triangle
  • Bright-angled triangle
  • Cacute-angled triangle

Q3:

What do we call a triangle that has angles 8 0 ∘ , 6 8 ∘ , and 3 2 ∘ ?

  • Aan obtuse-angled triangle
  • Ba right-angled triangle
  • Can acute-angled triangle

Q4:

Suppose that, in β–³ 𝐴 𝐡 𝐢 , 𝐴 𝐡 = 1 3 cm, 𝐡 𝐢 = 3 6 , and 𝐴 𝐢 = 3 5 . What kind of triangle is this, in terms of its angles?

  • AIt is an obtuse-angled triangle.
  • BIt is a right-angled triangle.
  • CIt is an acute-angled triangle.

Q5:

Suppose that 𝐡 𝐢 = 2 6 c m and 𝐷 𝐢 = 3 8 c m in the figure. What kind of triangle is β–³ 𝐡 𝐢 𝐷 , in terms of its angles?

  • Aacute-angled triangle
  • Bright-angled triangle
  • Cobtuse-angled triangle

Q6:

In triangle 𝑋 π‘Œ 𝑍 , ( 𝑋 π‘Œ ) = ( π‘Œ 𝑍 ) + ( 𝑍 𝑋 ) 2 2 2 . What type of angle is 𝑍 ?

  • Aacute
  • Bobtuse
  • Cright

Q7:

In triangle 𝐴 𝐡 𝐢 , ( 𝐴 𝐡 ) = ( 𝐴 𝐢 ) βˆ’ ( 𝐡 𝐢 ) 2 2 2 . What type of angle is 𝐢 ?

  • Aright
  • Bobtuse
  • Cacute

Q8:

In triangle 𝐴 𝐡 𝐢 , ( 𝐴 𝐢 ) βˆ’ ( 𝐴 𝐡 ) = ( 𝐡 𝐢 ) βˆ’ 3 2 2 2 . What type of angle is 𝐡 ?

  • Aright
  • Bobtuse
  • Cacute

Q9:

In a triangle 𝐷 𝐸 𝐹 , π‘š ∠ 𝐷 = 2 6 ∘ and π‘š ∠ 𝐸 = 1 2 π‘š ∠ 𝐷 . In terms of the measures of the angles, what is the type of the triangle?

  • Aacute-angled
  • Bright-angled
  • Cobtuse-angled

Q10:

In the figure, is a rectangle. Determine what type of triangle is, in terms of the measures of its angles.

  • Aobtuse-angled triangle
  • Bright-angled triangle
  • Cacute-angled triangle

Q11:

Given that 𝐴 𝐢 = 2 2 c m , what type of triangle is β–³ 𝐴 𝐡 𝐢 in terms of its angles?

  • Aobtuse-angled triangle
  • Bright-angled triangle
  • Cacute-angled triangle

Q12:

A triangle 𝐴 𝐡 𝐢 has side lengths 𝐴 𝐡 = 6 c m , 𝐡 𝐢 = 8 c m , and 𝐴 𝐢 = 1 0 c m . By drawing a picture or otherwise, find the measure of ∠ 𝐴 𝐡 𝐢 .

Q13:

In β–³ 𝐴 𝐡 𝐢 , 𝐴 𝐡 = 9 , 𝐡 𝐢 = 3 6 , and 𝐴 𝐢 = 3 4 . What kind of angle is ∠ 𝐴 ?

  • Aacute
  • Bright angle
  • Cobtuse

Q14:

Which of the following is true of triangle 𝐴 𝐡 𝐢 ?

  • AAll its angles are acute.
  • BIt is a right-angled triangle.
  • CIt has an obtuse angle.

Q15:

In the given figure, is a quadrilateral in which , , , and . What type of triangle is in terms of the measures of its angles?

  • Aright-angled triangle
  • Bobtuse-angled triangle
  • Cacute-angled triangle

Q16:

Given that 𝐴 𝐡 𝐢 𝐷 is a rhombus in which 𝐴 𝐢 = 4 6 c m and 𝐡 𝐷 = 4 0 c m , what type of triangle is β–³ 𝐴 𝐡 𝐷 , in terms of its angles?

  • Aa right-angled triangle
  • Ban obtuse-angled triangle
  • Can acute-angled triangle

Q17:

What do these shapes have in common?

  • ABoth are isosceles triangles.
  • BBoth are right triangles.
  • CBoth are acute triangles.
  • DBoth are triangles.
  • E Both are equilateral triangles.

Q18:

In triangle 𝐴 𝐡 𝐢 , 𝐴 𝐡 = 1 0 . 6 c m , 𝐡 𝐢 = 2 9 c m , and 𝐢 𝐴 = 2 1 . 9 c m . Classify β–³ 𝐴 𝐡 𝐢 by the types of its angles, and then decide whether the centre of its circumcircle is inside or outside the triangle.

  • Aright-angled triangle, on the triangle
  • Bacute-angled triangle, inside the triangle
  • Cobtuse-angled triangle, outside the triangle

Q19:

In an obtuse triangle, are all the angles obtuse angles?

  • A no
  • B yes

Q20:

In any triangle, there are at least two angles.

  • A obtuse
  • B right
  • C equal
  • D acute

Q21:

Can a triangle have three acute angles?

  • A yes
  • B no

Q22:

Can a triangle have both a right angle and an obtuse angle?

  • A no
  • B yes

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