Worksheet: Types of Triangles: Angles

In this worksheet, we will practice classifying triangles based on their angles to acute, right, or obtuse.


Given that 𝐴𝐡𝐢 is a triangle in which π‘šβˆ π΄βˆΆπ‘šβˆ π΅βˆΆπ‘šβˆ πΆ=4∢5∢6, determine the triangle’s type in terms of its angles without finding their measures.

  • Aobtuse-angled triangle
  • Bacute-angled triangle
  • Cright-angled triangle


Suppose that, in △𝐴𝐡𝐢, 𝐴𝐡=13 cm, 𝐡𝐢=36, and 𝐴𝐢=35. What kind of triangle is this, in terms of its angles?

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


Suppose that 𝐡𝐢=26cm and 𝐷𝐢=38cm in the figure. What kind of triangle is △𝐡𝐢𝐷, in terms of its angles?

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


In triangle π‘‹π‘Œπ‘, (π‘‹π‘Œ)=(π‘Œπ‘)+(𝑍𝑋). What type of angle is 𝑍?

  • Aacute
  • Bright
  • Cobtuse


In triangle 𝐴𝐡𝐢, (𝐴𝐡)=(𝐴𝐢)βˆ’(𝐡𝐢). What type of angle is 𝐢?

  • Aobtuse
  • Bright
  • Cacute


In triangle 𝐴𝐡𝐢, (𝐴𝐢)βˆ’(𝐴𝐡)=(𝐡𝐢)βˆ’3. What type of angle is 𝐡?

  • Aright
  • Bacute
  • Cobtuse


In a triangle 𝐷𝐸𝐹, π‘šβˆ π·=26∘ and π‘šβˆ πΈ=12π‘šβˆ π·. In terms of the measures of the angles, what is the type of the triangle?

  • Aobtuse-angled
  • Bacute-angled
  • Cright-angled


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

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


Given that 𝐴𝐢=22cm, what type of triangle is △𝐴𝐡𝐢 in terms of its angles?

  • Aacute-angled triangle
  • Bobtuse-angled triangle
  • Cright-angled triangle


A triangle 𝐴𝐡𝐢 has side lengths 𝐴𝐡=6cm, 𝐡𝐢=8cm, and 𝐴𝐢=10cm. By drawing a picture or otherwise, find the measure of ∠𝐴𝐡𝐢.


In △𝐴𝐡𝐢, 𝐴𝐡=9, 𝐡𝐢=36, and 𝐴𝐢=34. What kind of angle is ∠𝐴?

  • Aobtuse
  • Bacute
  • Cright angle


In the given figure, 𝐴𝐡𝐢𝐷 is a quadrilateral in which 𝐴𝐡=140, 𝐡𝐢=105, 𝐢𝐷=180, and 𝐷𝐴=103. What type of triangle is △𝐴𝐷𝐢 in terms of the measures of its angles?

  • AObtuse-angled triangle
  • BAcute-angled triangle
  • CRight-angled triangle


Given that 𝐴𝐡𝐢𝐷 is a rhombus in which 𝐴𝐢=46cm and 𝐡𝐷=40cm, what type of triangle is △𝐴𝐡𝐷, in terms of its angles?

  • Aan obtuse-angled triangle
  • Ban acute-angled triangle
  • Ca right-angled triangle


In a triangle 𝐴𝐡𝐢, 𝐴𝐡=10.6cm, 𝐡𝐢=29cm, and 𝐢𝐴=21.9cm. Classify △𝐴𝐡𝐢 by the types of its angles, and then decide whether the center 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


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

  • Ayes
  • Bno


In any triangle, there are at least two angles.

  • Aequal
  • Bobtuse
  • Cacute
  • Dright


Can a triangle have three acute angles?

  • Ano
  • Byes


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

  • Ano
  • Byes


If the length of two sides of an isosceles triangle are 3 cm and 4 cm, what type of angle is the largest angle in the triangle?

  • Aobtuse
  • Bacute
  • Cright


Complete the following: Any triangle has at least acute angles.


Is it possible to draw a triangle with two obtuse angles?

  • Ano
  • Byes

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