# Worksheet: Types of Triangles: Angles

In this worksheet, we will practice classifying triangles as acute, right, or obtuse by considering the size of their angles.

Q1:

Given that is a triangle in which , determine the triangle’s type in terms of its angles without finding their measures.

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

Q2:

Suppose that, in , cm, , and . 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.

Q3:

Suppose that and in the figure. What kind of triangle is , in terms of its angles? • Aobtuse-angled triangle
• Bright-angled triangle
• Cacute-angled triangle

Q4:

In triangle , . What type of angle is ?

• Aacute
• Bright
• Cobtuse

Q5:

In triangle , . What type of angle is ?

• Aobtuse
• Bright
• Cacute

Q6:

In triangle , . What type of angle is ?

• Aright
• Bacute
• Cobtuse

Q7:

In a triangle , and . In terms of the measures of the angles, what is the type of the triangle?

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

Q8:

In the figure, is a rectangle. Determine what type of triangle is, in terms of the measures of its angles. • Aobtuse-angled triangle
• Bacute-angled triangle
• Cright-angled triangle

Q9:

Given that , what type of triangle is in terms of its angles? • Aacute-angled triangle
• Bobtuse-angled triangle
• Cright-angled triangle

Q10:

A triangle has side lengths , , and . By drawing a picture or otherwise, find the measure of .

Q11:

In , , , and . What kind of angle is ?

• Aobtuse
• Bacute
• Cright angle

Q12:

In the given figure, is a quadrilateral in which , , , and . What type of triangle is in terms of the measures of its angles? • AObtuse-angled triangle
• BAcute-angled triangle
• CRight-angled triangle

Q13:

Given that is a rhombus in which and , what type of triangle is , in terms of its angles?

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

Q14:

In a triangle , , , and . Classify 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

Q15:

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

• Ayes
• Bno

Q16:

In any triangle, there are at least two angles.

• Aequal
• Bobtuse
• Cacute
• Dright

Q17:

Can a triangle have three acute angles?

• Ano
• Byes

Q18:

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

• Ano
• Byes

Q19:

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

Q20:

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

Q21:

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

• Ano
• Byes